Arrow velocity

[James Park]

To go with the new arrow velocity program, I need to cover a couple of definitions.
The first is "Fill percentage".
http://www.archery-forum.com/4sale/20021103194742.jpg
A 100% fill would be a force-draw curve that extracted the maximum possible energy from the bow for a given maximum draw weight, draw length and brace height. The force-draw curve would go straight up, straight across at maximum weight and then straight down at full draw to the holding weight. That is: the area under the curve would be the maximum you could get. The stored energy would in that case be the maximum force multiplied by the stoke length.
The actual fill percentage for a given bow is what percentage of the above 100% bow the force-draw curve actually fills. In the case of the Quantum above, the area under the force-draw curve is about 67% of the maximum possible for its draw weight, draw length and brace height.
A hatchet cam bow would fill in more of the space and hence have a higher fill percentage.
A round wheel bow would fill in less of the available space and have a lower fill percentage.
To measure the fill percentage you need to accurately plot the force-draw curve for your bow. To do this you need to have a tape measure, a spring balance, and a person to help you. It is then reasonably straightforward.

[James Park]

The second definition required is of "Virtual Mass".
When you draw the bow you store energy. Not all of this energy gets to the arrow after the release, some of it is lost. A well established way of describing this is by the use of "Virtual Mass".
The way this works is that after release some of the stored energy of the bow is used to accelerate the arrow up to its final speed. The amount of energy that is lost could be described as being used to accelerate an effective mass of the moving parts of the bow (the "Virtual Mass").
So: the energy stored in the bow is split between the actual arrow mass and the bow's "Virtual Mass".
The arrow energy proportion is: (arrow mass)/(arrow mass + Virtual Mass).
The wasted energy proportion is: (Virtual Mass)/(arrow mass + Virtual Mass).
That is, the lower the arrow mass in proportion to the Virtual Mass, the lower the proportion of the bow's stored energy that ends up with the arrow. The lower the Virtual Mass, the more efficient the energy transfer will be, and the faster the bow.
The Virtual Mass is determined by many things: the mass of the string and other moving parts such as the limbs, cams and wheels, air resistance of the limbs, material losses in the limbs, etc.
You cannot measure the Virtual Mass directly. It is best measured by first measuring the fill percentage and the energy stored by the bow, and then measuring the velocity of an arrow of known mass. You can then calculate the Virtual Mass of the bow.

[James Park]

Third, we need to calculate the available energy from the bow:
To get this, you take the bow weight, multiply it by the stroke length (draw length - brace height), and multiply that by the fill percentage.

Then, to get the arrow energy, use the formula from the post above, with the bow energy. That is:
arrow energy=bow energy x (arrow mass)/(arrow mass + Virtual Mass).

Once you have the arrow energy you can calculate the arrow velocity:
velocity = square rooot of (2 x arrow energy / arrow mass)

And there you have it !! This is exactly what the new program does, and the reason why fill% and Virtual Mass are important.

In the program I do all the calculations in metric units (Metres, Kilograms, Newtons, seconds), and then (so that the archery world can understand it) change it all into ft/sec, inches, grains and pounds.

[Marcus]

The new program can be downloaded from

http://www.archery-forum.com/free/arrowvelocity.zip

Excellent program!

[GrahameA]

Marcus

Is the arrow velocity programme still available? The link is not working for me.

[reversehaven]

yeah. the link ain't working for me either. is it still available?

[Marcus]

I'll get it back on the server soon.

[GrahameA]

Evening Marcus

Thank you.