Aerodynamic drag

[James Park]

A number of archers have asked me about aerodynamic drag and how it is calculated.
The general formula for drag is: D=Cd*Area*(Velocity squared).
That is, the drag increases in proportion to the area over which the air is moving, and in proportion to the square of the velocity. That is: twice as fast means four times the drag.
Cd is the drag coefficient, and it is a complicated parameter. There are two sorts of air flow: laminar (or smooth), and turbulent (or rough), and Cd varies dramatically depending upon which type of flow we have - it is generally much less for turbulent flow (and hence the dimples on golf balls to make them go further). For an arrow, the typical velocities mean that the air flow is virtually always turbulent, which is good.
For an arrow, we need to consider the contribution to drag from four parts: the arrowhead, the shaft, the fletches and the nock. Cd is different for each part, and needs to be calculated individually for each part for the particular velocity concerned - it is a complicated calculation. The most complicated part to calculate is the nock.
Generally, the largest contribution to the arrow's total drag is the shaft area, followed by the fletches, followed by the nock, followed by the arrowhead. The shape of the arrowhead matters very little - it is mostly its cross sectional area that matters, and a totally blunt head has just about the same drag as a bullet-shaped head.
For my X10's shot from my PSE Quantum: the arrowhead contributes 2% of the drag, the shaft 84%, the fletches 7% and the nock 7%, so the shaft absolutely dominates.
Having calculated the actual drag force on the arrow, it is best to state it as a proportion of the arrow's mass (as is done in Accurate Sights): that is, in "G's". A drag force equal to the arrow's mass means a force of 1G.
To minimise the drag, you need a skinny, but heavy, arrow. That is why X10's are so good. For my X10's, the drag is 0.85G.
Note that in calculating an arrow's flight path to the target the drag force continually changes as the arrow slows down - that makes it a particularly challenging calculation (and is the reason why calculating the trajectory and maximum distance in Accurate Sights can take quite a time - this is very important in calculating the effect of errors in the arrow's mass, for example).

[Singerov]

Jim, the maximum distance of the arrow with my bow setup according to the AS software (v5.5.1) is 370m (V=82 m/s and angle=40 deg). Isn't this too short distance for such velocity ? I understand that air drag contributes to the overall distance but it can not slow down the arrow so much.
According to this formula for max. distance of projectile, x=[(Vo^2)*Sin(2*angle)]/G the max. distance x=675m, which is almost double the distance of 370m.
The time of flight is t=[2*Vo*Sin(angle)]/G = 10.7 sec which is very similar to the time calculated in the AS software (9 sec.)
Because of the air drag, velocity is not constant and the projectile's velocity at the impact is less than the velocity at start of the arrow's flight,
but does the air drag contribute so much for such diference in calculaton?
Arrow is pretty aerodynamic projectile so Cd is not that big to shorten the flight so much.
Can you please explain this ?

Thanks

[Joe]

With 82 m/s launch speed maximum range would be around 580 metres (arrow design dependant) so drag does result in a significant loss in range.

[James Park]

Zoran and Joe,
Yes, the drag really does make a very considerable difference. The drag is actually quite large (can be over 1 G), even though the arrow is quite a good shape.
I have tested the calculations quite carefully by comparing the calculated distances with actual flight distances, and they match very well.

[DrRalph]

Zoran and Joe,
Yes, the drag really does make a very considerable difference. The drag is actually quite large (can be over 1 G), even though the arrow is quite a good shape.
I have tested the calculations quite carefully by comparing the calculated distances with actual flight distances, and they match very well.

Jim.

Do you include vortex shedding and the Munk effect? It has been claimed that arrows can even exceed the 'vacuum ' distance. Arrows will often fly close futher than say a ball bearing the same diameter.

What is your opinion on:

http://homepage.ntlworld.com/joetapley/

DrR

[James Park]

DrR,
I will have a careful look at the site over the next day or so.
I have used simply models for drag, and then tested my calculations using both actual wind tunnel measurements done by others (as quoted by Liston, for example), as well as calculated vs actual flight shot distances for a range of arrows (as was also done by Liston). The agreement between my calculations, those of others, and flight shots has been quite good and sufficient to convince me that the accuracy is sufficient for such things as sight setting programs.
Where I suspect we can see some deviations is in extreme velocities with specialist flight gear, and in this respect I could see value in measuring the actual arrow velocities and using these in the calculations (but so far I have not succeeded in measuring these).

[recurve boy]

Vittorio Frangilli on the Sagi forum has done his own modelling and testing and has come to conclusion that the best arrows to shoot are those that have the lightest weight for the required spine, such that the heaviest point can be used.

Hence, by Vittorio's calculations and tests, the ACE is still the best shaft to use. i.e. light weight so I guess you can go up a couple spines then stick in a very heavy point. Of course it depends on particuler setups.

So, whose more right, Vittorio or James and whose modelling is more accurate?

[mike]

So, whose more right, Vittorio or James and whose modelling is more accurate?



Shouldn't be an issue. We're not dealling with theoretical physics here, just plain aerodynamics. One of them is right, the other is catagorically wrong. Thats the way physics works.

[Aarleks]

I must say that I agree with both to certain extents. Certainly for two arrows of the same weight and similar diameter I would prefer the one with the heavier point or higher FOC. In that respect I believe Vittorio is correct. However, in the case of ACE Vs Triple in the wind, the sheer weight difference does come into it. Unless you are shooting the higher (lower?) spines of ACE (ie 520 plus with 120gr points) the Triple will win the wind-drift competition everytime. For Vittorio what is important is high FOC. This means heavy points (125gr for Michelle) and so, as you say Marc, a higher spine and thus heavier shaft.

I was witness to the difference on Saturday at Homebush (ranking round). Using Accurate Sights I have calculated the average wind at my shot (ie the lowest points in the wind) was 19kph. Also calculated gusts up to 22kph for some shots (even higher when not shooting!! :o ). In this wind I was still able to group reasonably well compared to my target-mate (although I was still crap :roll: ) who used ACEs and is a nominally better archer than me. For him shooting in that wind at 90m was pot luck, for me not. I put some of that down to my heavy (349gr) arrows.

The shoot was eventually called off after a target full of arrows was blown over (one of SIAPs practice ones so only club alloys thankfully). Whilst we were meeting to vote on this one of our targets which we had just pulled arrows from blew over... That decided it. Had we been shooting as we should have at that point there would have been around $900 worth of arrows destroyed in one fell swoop. Damn wind deities :agrue: :o

Of course for the average recurver the issue of 90m sight marks comes into it. I can't reach 90m with my sight fully extended. With ACEs I could. Of course for people like you and me Marc, the difference is small. Probably only two centimeters drift at 70m due to the extra speed of the ACE...

[recurve boy]

Even with physics you must consider what the best way to model the arrow is - which forces contribute significantly and which can be ignored. If you get this wrong, while the physics may be strictly correct, you'll get the wrong answer. Obviously James and Vittorio are using different approaches since their final conclusions differ - or they have different priorities. To some degree both are right. But whose approach is better?

I am not concerned about how good I am and what difference it will make, rather what would be the theoretical best setup for me so that I don't have to go on making equipment changes. I hate making major changes, waste of my time.

Does Accurate Sights generate graphs of wind drift for a particular bow setup for various acceptable arrow configurations? So drift vs point weight vs shaft spine (hence weight, diameter). That would be useful. We could then just compare performance over a whole range of arrow configs and pluck out the best one.

[mike]

Its the physics that defines the models, not the other way around.

An arrow is an arrow, there are only certain things that can happen to it and these can be calculated (which is similar to modelling, but more accurate). All you need is the properties of the arrow (which are readily measurable) and the speed at which it begins its flight. So, really, the answer should be simple, and as Jim will no doubt say, the result is that you want the arrow to be heavy and thin and fast. The more you optimise these the better for wind drift. In almost all circumstances a heavier arrow will outperform a lighter one given the same speed and mass. Also, a faster, lighter arrow will often not outperform a slower thinner and heavier arrow.

Net conclusion -- shoot X10s for target, they will outperform any other arrow in the wind.

Of course if the ACEs that Michelle Frangilli uses are expertly tuned for his set up, they may score better than a worse tuned X10 -- this stands to reason but it is not a good reason to choose ACEs over X10s. Michelle could beat most people with X10s too.

[Aarleks]

Well said Mike. :D

I think Frangilli is an exception to the rule, and in many ways. His draw sequence immediately comes to mind :o . Bear in mind that he shoots 430 ACEs@ 29.6" with 125gr points and heavy Beiter nocks. That gives him around a 354gr arrow, more than enough to cope with any wind, and at his poundage (51# if I remember correctly) he is probably getting around 220fps+ which is very fast for a recurve. The equivalent sized X10 would give him around a 377gr arrow resulting in a much slower (still 216fps - much faster than my setup :o ) arrow. However, Accurate Sights still tells us that the X10 would outperform the ACE in the wind, even though it might be up to 10fps slower. Perhaps Frangilli is more concerned with narrower sight marks (for form reasons - only 7cms between 30m and 90m?) and a higher FOC (as is Vittorio's reasoning) than pure wind-drift performance. Who knows... They claim to have done testing to determine which they feel is best for him. Can't do any more than that.

[recurve boy]

Its the physics that defines the models, not the other way around.

But is the correct physics* being used? As an analogy insects should not be able to fly if they are aerodynamically described using the physics that govern a plane. But the physics that describe planes is indeed quite correct. Insects fly as well but obviously must be explained using different physics.

So, while both people are trying to model arrows and the physics is unlikely to be vastly different, obviously James and Vittorio are doing things differently. Now, what is different and what are the merits of each approach? Thinner and heavier may be a nice rule of thumb but I firmly believe that the Frangilli's did extensive testing. They certainly have the means to do so and would have tested X10s, ACEs, CTs ... they found that for Michele, the ACE out performed the rest. There is simply no need for what they "feel" is the best, they just go and find out. If X10s are the best, do you really think they would have used a lesser arrow? Why would you do that if you could afford the best? That's crazy.


*I think perhaps I shouldn't use "model" and "physics" to mean the same thing anymore... but you see what I mean I hope.

[mike]

Well, yes it is critical that the correct physics is being applied and also important that it is applied in the correct way.

What I have not seen is a description of the physics behind the testing that the Frangillis have done.

You see, the thing is that if Michelle Frangilli, through testing alone, has decided upon the ACE, then that is all well and good for Michelle Frangilli. It does not by itself provide a formula for working out what is the best arrow for anyone else.

If, on the other hand, the Frangillis have calculated the aerodynamics of the arrows in question then verified or otherwise these calculations by testing, then those calculations that bare themselves out in testing can be used by other archers. This is what Jim has done in AS for normal archery conditions (hence the Flight exception).

Like I said, the Frangillis have found an ACE setup that works brilliantly. I suspect they could also find an X10 setup that also works just as well. It would be my contention that the X10 could actually be better, but might require an equivalent amout of testing and experience, which in the case of the Frangillis and ACEs, is YEARS.

So, its ACEs for the Frangillis, I'm just saying that you want something more than individual testing for general application.

[James Park]

As noted by Mike, there is only one set of physics, and we all need to live with it. In thinking about such things as drift, etc, the skill is in knowing how to best to model it. The maths is inevitably complicated and usually non-linear, so there is definitely scope for different approaches.
I think it is very important to do the modelling and then to have some strong tests that help determine the validity of your approach - this is what I have done in using flight archery tests versus calculated maximum distances from my modelling, and this testing has given me confidence that my modelling is quite good. Note that I first calculated the expected flight shot distance and published my expected results, and then went and did the shots to test it, not the other way around. Also, to further test my modelling I made predictions for a range of arrow types and tested those as well.
What this leads me to think is the following (for target archery, where drift is the major factor):
- You do want a heavy arrow rather than a light arrow. This is because the heavy arrow extracts more energy from the bow (it is simply the arrow's mass compared to the bow's virtual mass that gives the energy split). Hence, I would use both a heavy arrow and a heavy point (and hence, X10's with full-weight tungsten points).
- You want a high energy bow, consistent with it still being easy to shoot. Hence, I would select a cam bow rather than a round-wheel bow, but with a reasonable brace height (say at least 7.5 inches). For example, my Primos STL has a high energy cam, but quite a good brace height.
- Given an arrow with a certain amount of energy, the drift is determined by the area of the arrow visible to the wind and the arrow's mass. This means that a smaller diameter arrow will drift less than a larger diameter arrow.
So, comparing an X10 and an ACE:
- The X10 should be heavier, and will extract greater energy from the bow.
- The X10 will have a smaller side area than an ACE. That, as well as the greater mass of the X10, will lead to less drift, even though the X10 will have a lower velocity (if you do the maths, which I have, this comes out quite plainly).
Hence, an X10 will always beat an ACE for drift.
Regarding FOC:
- The orientation of the arrow in a constant wind will always line up with the resultant vector of the two velocity components: the arrow's forward velocity and the wind velocity. That is, in a steady state the FOC will not matter.
- In a variable wind (that is, varying on a time constant of less than the time it takes for the arrow to get to the target), the FOC will influence how long it takes for the arrow to line up with the instantaneous resultant vector. In this circumstance you can get some steering effects from the arrow being slightly side-on to the resultant vector following a sudden wind change. In this circumstance it is possible to get negative drift, and it could be that in this respect that Frangili is finding some advantage. However, I do not think this is peculiar to an ACE, you could do the same with an X10.
Hence, if I were Frangili, I would still be looking to see if I could do better with an X10.
The other aspect that is worth considering is that an arrow has a natural resonant frequency, as well as a mass determined by its construction. The combination of this resonant frequency and mass determine how well it can be matched to a particular bow (its mass and the bow's force-draw curve determine the arrow velocity, and its resonant frequency determine how it flexes as it leaves the bow). I have suspected for a long time that a particular arrow construction might have a better combination of resonant frequency and mass than another, and that therefore you might get one arrow type inherently tuning better than another. However, I have not pushed the analysis in this area to a conclusion, but note that in the days long past an X7 size 2114 and a draw length of about 30" with a bow weight of about 50 pounds gave a wonderfully good combination - perhaps in this particular combination the resonant frequency and mass gave an optimum.
Hence, overall a complex area (but I still firmly believe the X10 to be the best with regard to minimising wind drift).

[recurve boy]

Hence, overall a complex area (but I still firmly believe the X10 to be the best with regard to minimising wind drift).
But unfortunately that's not what the testing shows (assuming it wasn't sloppy) :cry: :cry:

[James Park]

recurve boy:
My testing has certainly shown it (as well as having the maths show it).

[recurve boy]

Sorry :oops: I meant the Frangillis' testing. I believe what you have done. It makes sense. I am having trouble trying to resolve what Vittorio said :(

Ah well, back to the drawing board for me.

[Marcus]

Recurve Boy
It would be of huge gelp if you post a link to this info by Frangilli. Perhaps then Jim can analyse it and find out how he came to his conclusion.

[Joe]

If one were writing an arrow design guide then rule number 1 would be along the lines of:

1. A heavier shaft is the kiss of death for a target arrow

As far as X10 v ACE goes, back of the envelope (boe) calculations support Vittorio's conclusions.

Though no flight model exists that can predict wind effects on an arrow
with any accuracy the boe approach suggests that as far as arrow response to wind/wind gusts go the X10 and ACE are pretty even steven - comes down to a few grains of pile weight. Factor in the ACE arrow being lighter and hence faster plus the better grouping from the lighter shaft (rule no 1) and the ACE looks the better bet.

Boe calcs are just that. Only testing for real ultimately matters.

[James Park]

One important point I should have included in my post above:
- While it is arrow energy that matters, not arrow velocity, not all arrows are equal on down-range arrow energy.
- If you have two arrows starting with the same energy (and remember that the heavier X10 will actually extract more energy from the bow than the lighter ACE), the arrow with the lower aerodynamic drag will retain that energy much better than the other.
- That is: because the X10 have a lower drag than an ACE, the X10 will retain its energy much better than the ACE.
- This quite significantly contributes to less wind drift for the X10.
This can be quite easily demonstrated in flight shots: I have shot X10's and ACE's using the same bow, and the X10's went further (430M vs 400M) even though they had significantly lower initial velocity. That is: don't confuse energy with velocity - it is the energy and the drag that matter, and faster is not necessarily better.
I do realise that the higher velocity ACE will get to the target in less time than the X10, but in that time it will lose more energy than the X10 and will drift further in a side wind.

[Marcus]

So it's an opinion piece rather than an article detailing actual tests done. :roll:

[recurve boy]

Yes, but it is based on the tests/modelling he did. Why would he lie about his results? That's stupid.

[James Park]

If you simulate with computer programs all possible combinations of arrows/spines/piles/foc suitable for men use (in the >29" draw and >48# area), you will easily find that the the balance between the desired foc and speed to get the highest Kinetic energy is verified by ACE's, only.
Things are different at shorter draw lenghts and lower poundages.
........... in field the lightest arrow wins (ACE), and in the wind the arrow with the best foc wins (ACE again).


and:


Intuition does not give you any practical result. Lighter shaft for the requird spine is ever better, as it allows you to use an heavier pile. The total weight of the arrow must be as much as possible in the point, not in the shaft. Only element against ACE is that at certain draw lenghts and poundages, other shafts are LIGHTER.


If it is kinetic energy that Vittorio is after then the answer is obvious: you must use the heaviest arrow. Here the physics is quite straightforward: the stored energy is the area under the force-draw curve and the amount of energy transfered to the arrow is simply dictated by how heavy the arrow is compared to the bow's virtual mass. I heavy arrow always gets more energy than a light arrow. Here, the X10 will certainly win, as they are heavier than ACE's.
Once you have the kinetic energy, if retaining it is the desire, then the answer is also obvious: you must use the arrow with the lowest drag.
For field, I agree with Vittorio, you want a very light arrow to get speed, and the ACE is a good selection.
While he states that FOC is the important factor in wind, we need to see his reasoning. Even if FOC is important, a heavy and small diameter arrow is also a key, and I can see good advantage in X10's for both of these.
So: why is FOC important???

[Marcus]

Yes, but it is based on the tests/modelling he did. Why would he lie about his results? That's stupid.
Because he developed a theory that he is unprepared to let go of and tests in a manner that supports his claims. For example when X10's came out he may has said "pfft, too slow, you need a fast arrow to cut through the wind" then in testing they found that Michele groups better with ACE's for some reason (most likely setup) and thus he has 'proven' his theory without actually having numbers.
Sorry but without proof we have nothing. He may well be right. This happens in science all the time, people work for years to prove their own theory correct, despite testing proving otherwise.

[Zoe]

You're not suggesting a "if at first you don't support your hypothesis, try try again" mentality are you Marcus? Cynical boy, this doesn't happen in the real sciences!

I'm predicting a great dissertation by Mike on FOC and reverse drift. He has been practicing at the dinner table (to snoring ovation). I think he's saving it for post #30,000.

Question has to be raised about having archers (brilliant as they are) doing the practical tests for you. Surely when you're talking about such minutae of differences in the outcome (and I'm sure Fragilli would have had his bow impeccably tuned for all scenarios), then certain mental variables come into play anyway ("what is this new-fangled arrow, I'm not convinced it will work, ho hum, lets give it a shot"...flinch!) - which gives credence to the whole 'shoot what you're comfortable with' argument. Although unscientific, perhaps a significant impact on scores at that level???
Perhaps not.
Bring it on Mike

[Marcus]

"if at first you don't support your hypothesis, try try again"
I've bought this up with Erika before when she's come home having finally got an experiment to work, thus proving the hypothisis correct and I'ld say "What about the 400 failed experiments before it, surely a 0.25% success rate is not replicatable" and I'm told "that's how science works"
Who am I to argue.

[mike]

Ok ok.... I'll have another crack at this problem :roll:

Lets leave the actual effect of the drag/wind on the arrow for the moment and just look at the forces on the arrow in flight (that way we can conveniently ignore the arrow's kinetic energy for the time being)

In dead still conditions, the forces are just drag (proportional to the effective surface area of the arrow) and gravity.

In wind, it is the above plus a side force from the wind (also proportional to the arrow's effective surface area) However, you must realise that the effective surface area of the arrow is not neccesarily the same for drag and wind force.

IF the arrow has a positive FOC, it will rotate such that the fletches are 'down wind'. This will introduce another force, call it the resistance force, that operates in the oposite direction to the wind force. This force will be in proportion to the speed of the arrow and the effective surface area. The higher the FOC, the greater this force will be. However as you increase the FOC, you increase the torque applied by the fletched end of the arrow, and so the arrow straightens up a little.

SO, the net force on the arrow will be proportional to:

The arrow speed, the wind speed and the effective surface area.

The direction of the action of this force will be the vector sum of these forces. Generally that will act in the down wind direction, and so small surface area is best and is the only way to optimise this situation.

[mike]

The effect of the force is a function of the amount of energy transfered into the arrow from the bow (as Jim said...). This is increased with heavier arrows.

More energy transferred = smaller effect of drag forces.


So, thus far, yet to see a compelling argument for ACEs over X10s, as the above still suggests that a combination of reduced net force from a thinner arrow and increased energy from a heavier arrow means that an X10 will have better aerodynamic properties and therefore will perform better in the wind.

Jim (and I) must be missing something that Vittorio has discovered...

[Aarleks]

Jim (and I) must be missing something that Vittorio has discovered...

No, I think you are both correct, and that Zoe and Marcus are also onto something. I think what we are seeing in the Frangilli's findings sugests, as has been said previously, that Michelle shoots better with ACEs. Their tests have probably quite conclusively proved this. However, this in no way proves the ACE is better than the X10 wind-wise.

[DrRalph]

Joe Tapley at the site I mentioned earlier has this to say about FOC and shaft drag:

The principle drag effect on the arrow which makes you 'miss' with a bad shot or a gust of wind is the drag on the shaft. The drag area of the shaft with respect to moving the arrow about depends on the arrow FOC. If 'L' is the length of the arrow shaft and 'A' its diameter then the shaft area Fa which relates to drag movement of the arrow is approximately given by:-
Fa = LA(1-FOC/50)

This is only an approximation because any rotation (fishtailing) of the arrow will affect the value of the shaft drag area.

e.g if the arrow is 80 cm long and has a 0.5 cm diameter then:-
with an FOC of 8% the shaft drag area is around 80 x 0.5(1-8/50) = 33.6 square cm

with an FOC of 16% the shaft drag area is around 80 x 0.5(1-16/50) = 27.2 square cm

or to put it another way each 1% increase in FOC reduces the shaft drag area by about 2%.

Seems to me that the italians are compensating for larger ACE shaft diameter by using much larger FOCs (ie very heavy tips). You could go for large FOC on X10, but end up with extremely heavy arrows suitable only for 60 lb compound archers :) My guess is high FOC for Michelle make his ACEs competitive with x10s with lesser FOCs for the same arrow weight overall.

R

[DrRalph]

Also from the UK site on FOC, that seems to be appropriate here. Personally I'd like to seem some detailed aerodynamic, as opposed to ballistic, modelling on this one. I think there is truth in both the 'thin x10' and'large FOC ACE' cases, and for different bow set ups one will be more important than the other. :

The overall speed of response of the arrow to fletching torque (its angular acceleration), i.e. how fast it straightens up, depends not only on the area of the fletchings but on the fletching torque and the 'rotatability' of the arrow, its moment of inertia. As the FOC increases the effective fletching area increases and the 'lever arm' increases.

Overall the arrow fletching response increases with FOC.

Having a higher FOC results in faster energy dissipation (more fletching action) and because the drag area moving the arrow is smaller the amount the arrow direction is changed is reduced. The result is more forgiving arrow to bad tuning or a poor shot leading to reduced group sizes. In a wind the smaller drag area that moves the arrow results in reduced wind drift.

The downside to a higher FOC is because the offset angle between the arrow axis and the direction it's going will in general be smaller, the drag on the pile will increase; lift from shaft drag will be reduced and probably the arrow will be heavier and hence going at a lower speed. All these factors result in 'loss of sight mark'.

[mike]

or to put it another way each 1% increase in FOC reduces the shaft drag area by about 2%.

Seems to me that the italians are compensating for larger ACE shaft diameter by using much larger FOCs (ie very heavy tips). You could go for large FOC on X10, but end up with extremely heavy arrows suitable only for 60 lb compound archers :) My guess is high FOC for Michelle make his ACEs competitive with x10s with lesser FOCs for the same arrow weight overall.

R

I think that this may be the case. At the end of the day, if you can afford to go out and test until you find the set up that works for you best, then that is the ideal way to go.

All this modelling is just about giving the average archer the tools needed to attempt to make a good choice first time.

The drag area of the shaft with respect to moving the arrow about depends on the arrow FOC. If 'L' is the length of the arrow shaft and 'A' its diameter then the shaft area Fa which relates to drag movement of the arrow is approximately given by:-
Fa = LA(1-FOC/50)

This is only an approximation because any rotation (fishtailing) of the arrow will affect the value of the shaft drag area.

Hang on, the drag area of the arrow can only change if it is rotated from the line of flight, and this requires a change in wind conditions. Increasing FOC gives the fletches greater mechanical advantage in that rotation. So the above equation either does describes it or it doesnt. We need more info on the derivation.

We need a dissertation from Joe and Vittorio!

[James Park]

It is still not clear to me why FOC gives an advantage. What is the physics behind that formula?
One thing does seem clear to me however - the arrow will line up with the resultant vector of the two components of the wind (the arrows forward motion through the air + the wind), it will not fly at an angle to this resultant other than temporarily due to a wind change. In steady-state conditions, the arrow will not plane through the air, although it might temporarily due to a gust of wind requiring it to move to a different orientation to line up with the instantaneous wind vector.
It seems to me that the FOC arguement is saying that the arrow does not line up with this wind vector. How so?

[DrRalph]

It seems to me that the FOC arguement is saying that the arrow does not line up with this wind vector. How so?

I think you are onto something. The argument seems to be that the arrow never does quite line up in a dynamical model. I can understand this in the vertical plane, because the arc is a curve and the arrow is continously rotating, as the tip starts out going up and ends up going down. What I don't also understand is how this applies with a *steady* horizontal wind. In a gusting wind maybe large FOCs allow the arrow to minimize the wind effects more quickly??? In a steady wind though it should adjust horizontally and stay there , as long as your FOC is good enough at all.

R

[James Park]

DrR,
Yes, in a steady wind, it simply has no choice but to line up with the resultant vector.
In a changing wind it will be continually trying to line up with the instantaneous vector and you will get some lateral movement of the arrow due to planing. It is here that you can get negative drift and positive drift due to "standard drift", and there have been thoughts that maybe you can get these to cancel (but I think that it is expecting too much to be able to find an optimum here).

[recurve boy]

Well, how often do you get steady winds? I would think that a perfectly uniform wind between you and the target is unlikely to ever happen.

[Joe]

Dear me you have been busy!

While it is arrow energy that matters, not arrow velocity...

James you've got this back to front. The "the heavier arrow retains it down-range energy" spiel is practically a piece of archery mythology. Think of it this way. A man starts with $100 and spends $20. Another man starts with $80 and spends $10. Who ends up with the most money? (i.e. speed).

the drag area of the arrow can only change if it is rotated from the line of flight

Mike - not correct. Confusion here about what is meant by drag area. If you rotate an arrow shaft from the line of flight the drag area remains exactly the same, what changes is the momentum transfer between the air and the shaft. Re the quote, drag on an arrow has different effects. To represent the drag on an arrow you need two force vectors one running through the arrow centre of mass and one which doesn't. The FOC defines how the overall shaft drag is proportioned between these two force vectors (which I describe in terms of shaft areas).

It is still not clear to me why FOC gives an advantage.

James - that's down to me for failing to give a clear explanation - I do my best. Very difficult to describe a complex mechanical system to people with little understanding of mechanics (poor excuse maybe).

"Fa = LA(1-FOC/50)

Mike/James - This formula gives you the approximate split between how the overall shaft drag divides between the two above mentioned force vectors. The physics behind the formula is given on my web site in the section on drag. To clarify - the section on arrow flight is supposed to be read sequentially so the section on FOC assumes you already know something about drag on the arrow. I obviously can't include a mechanics primer so maybe having an introduction to mechanics handy when reading the basic sections would come in handy.

"One thing does seem clear to me however - the arrow will line up with the resultant vector of the two components of the wind....it will not fly at an angle to this resultant.....

When trying to describe the behaviour of a complex system you inevitably have to make simplifications. What you need to be careful about is justifying the simplifications you make so you don't end up throwing the baby away with the bath water. The most damaging non-valid simplification that is made with respect to arrow flight is contained in the above quote. Unless you guys dump the 'straight arrow' simplification you're never going to get anywhere in understanding arrow flight behaviour.

Revurve Boy - whether you have a wind or not makes no difference to the above comment.

No offense intended by the above comments. I assume that the everybody's purpose is to get a beter understanding of archery.

[James Park]

Mike, do you want to fight or should I? :D

Joe, what is you web site URL?

[recurve boy]

I believe the URL is on the first page of this thread.

[Joe]

What I don't also understand is how this applies with a *steady* horizontal wind

DrRalph

Apologies, I missed that query.

Suppose you have a weight hanging from piece of string. You pull the weight sideways keeping the string taut and let go. What happens? The pendulum swings, the weight drops to its lowest point and then the weight stops dead at the lowest point. Yes? No of course not. The weight has gained KE so it keeps moving. It will only come to a stop if it manages somehow to lose all the useable potential energy it had to start with. Lets assume the arrow leaves the bow in a wind with initially zero potential or rotational energy (theoretically not impossible though in practice it never happens). The constant horizontal wind rotates the arrow (pulls the weight sideways) to some limit (let's pass on what that limit is!). Subsequently the arrow behaves just like the pendulum, it swings back and forwards.

James - a good compound archer v a mediocre recurve archer at 300 metres? - I surrender. :lol:

[DrRalph]

Thanks Joe.

I see what you mean, the drag alignment is not very well damped and it will oscillate, even in a steady wind. The whole process is dynamic even under steady conditions. I understood the fundamental vertical non alignment though :)

I love the Physics of Archery website BTW, as an astophysicist I haven't done a whole lot of aerodynamics - not an awful lot of drag in space - and it looks fascinating, and I'm going to take some more time to work through it all. Arrow flight has enough in it to become quite a subtle subject.

[mike]

Dear me you have been busy!

While it is arrow energy that matters, not arrow velocity...

James you've got this back to front. The "the heavier arrow retains it down-range energy" spiel is practically a piece of archery mythology. Think of it this way. A man starts with $100 and spends $20. Another man starts with $80 and spends $10. Who ends up with the most money? (i.e. speed).


This is challenging my (albeit undergraduate only) understanding of physics. The arrow can only have a certain amount of energy transferred to it from the bow. This energy absolutely dictates how fast the arrow will go (square root of (2*KE/m)).

The amount of energy transferred is a proportion of the stored energy of the bow, and it is proportional to the mass of the arrow divided by the (mass of the arrow - the virtual mass of the bow). Thus a heavier arrow extracts a greater proportion of the bows stored energy than a lighter one. Net result -- heavy arrow has more energy.

So, when shot out of the same bow, at the point of nock release from the string, a heavy arrow will have greater kinetic energy that a light arrow (even if a proportion of this is going to be lost through vibration).

It is this kinetic energy that determine what amount of force over a certain amount of time is required to achieve the equivalent movement of the arrow for different arrows (impulse).

The drag properties of the arrow determine how much force is available to produce this effect.

I have read your website Joe, and I think its is very good work, I certainly stuggle to dissagree, however I do struggle a little with the notion of arrows flying up wind. Also, what the site seems to lack is a treatment of the role of the energy transferred from the bow to the arrow in as much as it does change from arrow to arrow for the same bow (as discussed above).

Cheers

I think we need to have this discussion at a pub with some paper and pens!!

[DrRalph]

I think we need to have this discussion at a pub with some paper and pens!!

I think this is the best suggestion yet. Where and when :)

R

[James Park]

Joe,
An X10 does indeed retain its energy down range better than an ACE.
First, it starts with more energy than the ACE (because as Mike says, it is heavier and extracts more energy from the bow than the ACE).
Then, it has a significantly lower drag than the ACE (because it has a smaller diameter and is heavier). So: it slows down at a slower rate.
If you do the maths you can readily show that the X10 wins, and this is backed up by flight shots using the same bow, same draw length, an X10 and an ACE - the X10 goes further, even though its initial velocity is lower.

[DrRalph]

Jim,

Were the x10s and the ACEs the same weight - by putting a heavy tip on
a stiffer , heavier, (ie a 400) ACE? Then it would test FOC advantage vs smaller shaft drag more directly. If they were different masses then the energy efficiecy would affect the outcome, in addition to the different flight characteristics.

Clearly there is different evidence from your models and tests and the Frangilli's, but it is not so easy to compare the two without perhaps some systematic testing aimed at making the comparison and looking at just one issue: large FOC vs lower shaft drag overall.

I think Joe is right that the process is more dynamic than we are used to thinking, but it is not clear what the important timescales are and what the magnitude of the different effects are in the different cases we are discussing. From Jim's tests the ballistic+quadratic drag model is quite good in some (most?) cases. The lighter ACEs with large FOCs may just be a case where a more dynamic model is needed.

It would be great to get a mechanical shootng machine and do more tests along these lines.

On the otherhand, we could all just go and find what works for us, and concentrate on form.

[mike]

It would be great to get a mechanical shootng machine and do more tests along these lines.

On the otherhand, we could all just go and find what works for us, and concentrate on form.

Dammitt!! Someone always has to spoil a good esoteric discussion with practical considerations!!

Yes. It all means jack if you can't shoot the things properly, and lets face it, noone is perfect, so there will always be the chaos effect. (now I am really putting my foot in it potentially -- any chaos theorists out there?)

:D

[James Park]

DrR,
I am working on the basis that for a given bow the X10 will be heavier than the ACE.
However, even if they were the same mass the X10 will have lower drag because of its smaller diameter and this will give lower energy loss and less drift (assuming the FOC thing does not matter).
Sure we have to think a bit more widely than a purely static model with stable air flow, etc, and it is complex, but a few of Joe's comments don't gel with my "back of the envelope" first principles. I will, however, look carefully at his work, and if we can find better ways of understanding these things that would be good.

[Marcus]

James you've got this back to front. The "the heavier arrow retains it down-range energy" spiel is practically a piece of archery mythology. Think of it this way. A man starts with $100 and spends $20. Another man starts with $80 and spends $10. Who ends up with the most money? (i.e. speed).
Being an idiot web developer (little drag in webspace ;)) this comment does not sit well even for me. There is a reason why the US use depleted uranium in anti-tank munitions, it's heavy and dense, which equal great downrange velocity compared to a lighter projectile, and thus more energy is delivered to the target. Same in the ACE vs X10 debate. BTW Easton developed the X10 with this intent in mind, are you saying Joe that Easton's engineers are wrong?

Personally I have seen these effects just shooting at the club where an X10 will penetrate the target deeper than an ACE. Also worth noting a day in which I shot with an ACE shooter at 90m. We got our famous DVA drift at 90m and my heavy Triples moved into the 7, the ACE shooter was pushed into the 4. Having shot ACE's, X10's and Triples I have also found the same, my ACE's were the fastest, but drifted the most.

May mean nothing without the formula to back it up, but to this idiot the thin heavy arguement is logical, the FOC arguement is stretching. Maybe it's a recurve thing?

Anyway off to my comfort zone again and play with my variables.

[recurve boy]

All my physics studies have steered well away from classical mechanics and fluid dynamics and the like. I frankly suck at them. But from considering what is on Joe's website and _without_ taking them to be true:

1) Assuming that an X10 is always heavier than an ACE is a bad assumption. Perhaps it is OK if you go by charts or regular selection methods but who says we have to do that?

2) Arguements for using depleted uranium shells certainly do not apply to an arrow shaft. Such a shell would probably be very well described by highschool physics (I bet it approximates to a point mass quite well and we can ignore the majority of affects like drag). For an arrow, drag, turbulence etc should be considered as we can see from shooting an arrow, wind affects it a great deal.

3) Assuming an X10 will have less drag than an ACE is also a bad assumption. If the arrow was static and winds were steady I agree it is quite right but that is quite obviously not what the arrow is doing on the way to the target. There could be many characteristics of the shaft that could void this assumption as it flies through the air. But this is what I would have expected as well. But then many things you expect to be true are wrong.

Seems everybody is also having trouble accepting counterintuitive arguements. But intuition also says feathers always fall slower than bowling balls, and is totally useless when trying to explain quantum physics. Physics != intuitive.

[Joe]

While 'heavier mass arrow retains downrange velocity' is factually correct it is in practical terms a red herring. The following graphs relate to three identical arrows, other then overall mass, shot from the same bow. While the velocity difference between arrows changes the lighter arrow up to 90 metres always ends up better off.

http://homepage.ntlworld.com/joetapley/weight1.gif


http://homepage.ntlworld.com/joetapley/weight2.gif

[James Park]

Joe,
Your calculations do not match either my calculations or my experimental results.
Using my PSE Quantum, 60 pounds, 29", compound, I get the following, using X10 size 500 arrows weighing 339 grains and ACE size 520 arrows weighing 295 grains, both having the same fletches set at the same angles as well as the same nocks:

X10:
initial velocity 267 ft/sec (measured using a chrono as well as calculated by Accurate Sights)
velocity at 90M = 238 ft/sec
initial energy = 77.8 J
energy at 90M = 58.1 J
maximum distance = 417 M
initial drag = 0.85G

ACE:
initial velocity 282 ft/sec (measured using a chrono as well as calculated by Accurate Sights)
velocity at 90M = 244 ft/sec
initial energy = 70.6 J
energy at 90M = 52.8 J
maximum distance = 404 M
initial drag = 1.19G

I have carefully checked the flight distances in still conditions and the X10 very definitely goes further, in agreement with my calculations.

Noting that it is the arrow's energy, drag, and cross-sectional area that matters for drift, the X10 is very clearly better. The arrow's velocity is not important for drift (it is just a consequence of the arrow's energy and mass).

[DrRalph]

Personally I have seen these effects just shooting at the club where an X10 will penetrate the target deeper than an ACE. [snip] Having shot ACE's, X10's and Triples I have also found the same, my ACE's were the fastest, but drifted the most.

Don't discount experience, penetration should be a function of momentum and from Jim's measurements the X10s do have greater momentum at 90m. I also don't disagree that a higher drag ligher arrow will drift.

The odd question here seems to me is whether you can compensate for the drift a bit by using high FOC values, using a lighter arrow so that heavy points can be used and still keep the overall arrow mass down. It looked to me that it might be possible *in principle* from Joe's writings, (or in practice for Frangili) but as Jim pointed out it might be such a fine tuing excersise as to be impractical.

I'm glad to see the AS distance and speed calculations are supported by the experiements Jim. What were the FOCs on the arrows and what were the group sizes?

R

[James Park]

DrR:
X10's: size 500, mass 339 grains, point 110 grains
ACE's: size 520, mass 295 grains, point 85 grains
FOC's: never calculated them

Group sizes: not sure how to answer that one, but scored 1385 FITA with the X10's (and been over 1350 many times with them), 1355 is the highest I have got with ACE's.

Yes, I think it is very important to check some of the calculated parameters by experiment, it helps ensure you have not made some terrible blunder in the maths. Regarding drag: I would like to test that directly by wind tunnel measurement (and one reference I have has done that) but the best I have been able to do is the flight shots and seeing how well Accurate Sights predicts real sight settings. This has given me considerable confidence that my modelling is on the right track.
Regarding FOC and gusty wind: still thinking about it.

[Joe]

James

The point of the graphs I put up were to illustrate that the "heavier the the arrow dad de dah'. The arrows were IDENTICAL apart from the overall mass.

Your numbers don't agree or disagree with what I'm trying to say. When you compare an X10 with an ACE the arrows have different FOCs and diameters so you can't distinguish mass difference effects between them.

[bigfella]

Boy am I glad that I failed high school physics otherwise I may have pretended to understand all this!!

When all you fellas have worked out what happens and the best shaft for whatever conditions apply on any given day, pm me and let me know. Then I will go out and buy a dozen.

That way I will have prevented my brain from frying. :roll:

ps The forecast is for windy conditions in this weekend's SQAS target championships. Are my Triple 300's with 110 grns up front suitable?? Please keep your responses limited to fewer than 5000 words :roll: :roll:

[Jerrytee]

There will be a difference ( slight) between an arrow that weather cocks more quickly over one that does not but this difference will only be applied until the arrow settles into the apparent wind.

recurve boy reference you point 2 the equations of balistics that cover a depleted uranium anti tank projectile are exactly the same as those that cover an arrow shot from a bow. the only diferences are the scale of the numbers involved.Just for a laugh I would consider it theoretically possible that there is even a minute amount of paradox in the arrow like projectile. Considering how hard that thing is kicked up the backside when it leaves the barrel.

[whiz]

But is the correct physics* being used? As an analogy insects should not be able to fly if they are aerodynamically described using the physics that govern a plane. But the physics that describe planes is indeed quite correct. Insects fly as well but obviously must be explained using different physics.


Incorrect!

The limiting factor with describing how insects fly as compared to aircraft has been understood for a few years now. The classic example is "science doesn't know how bumblebees fly" when they have been modelled in heavy oil to explain where the extra lift comes from.
There are vortexes that weren't seen before that contribute the missing lift factors.
Now, addressing the aerodynamics involved.
(My history is of aircraft maintenance, advanced aeromodelling and an unhealthy interest in Low Speed airodynamics and aerodynes)

Lets say that we have a 100th scale model of a 747.

It will fly a lot more than a 100 times worse than a real 747.
The reason for this is that air becomes more like treacle, the smaller and slower you go. It doesn't flow around corners and just loses interest and wanders off like kids at the ballet.

Insects aren't so much flying, but more like dog paddling.

Radio control models are getting smaller and smaller and their wings are getting thinner and thinner. Nature is showing us the way...

Arrows have similar problems when describing the drag characteristics. They have massive variations in their Re (Reynolds numbers) throughout their flight.

There will be significant times where there is detached airflow behind the arrow shaft.
People haven't investigated invigorators to keep the airflow attached (as far as I know) but this could realise SIGNIFICANT drag reduction and speed retention.
Who's going to be the first to have little ridges and triangle spikes on their arrows?

I think that more research needs to be done.

If I'm bored, it might be me...

But I'll need a chronograph.
Actually, you probably will be able to see the different in horizontal grouping at distance.
Something to try...

[mike]

What would you have in mind regarding "invigorators" (I take it you are trying to encourage highly turbulent flow along the length of the arrow, and keeping it turbulent past the nock??)

Perhaps just wrap an arrow in sandpaper!!??

[whiz]

I wouldn't say highly turbulent flow. Just enough to keep it attached.
You'd have to do some experimentation but i doubt that you'd have to have sandpaper.
I'd start with some thick sewing thread wrapped in a wide spaced spiral
It would be easily done and reversible if you screwed it under the point and then wrapped it around and secured it at the nock.
If you shot six arrows at the longer distances with three spiral wrapped and three normal, you'd probably see the difference if they were enough to trip the separation point and reattach it.

There would be variables to eliminate and then you could perfect the trip strips to only where they would be needed.

Hmmm...

[The One]

vortexes

Vortices?

Yes, I agree with what you've said - Dragonflies are renowned (in much smaller physics circles!) for ustilising vortices from their front set of wings to provide extra lift on the second set that would not be possible otherwise.

[whiz]

Vortices?

Yes, I agree with what you've said - Dragonflies are renowned (in much smaller physics circles!) for ustilising vortices from their front set of wings to provide extra lift on the second set that would not be possible otherwise.

Sorry. Yes, Vortices.
Now I've got to ask you about "Ustilising"? :D

[The One]

Now I've got to ask you about "Ustilising"? :D

It's a spliced word of course, half-way between using and utilising :oops: