How far will my arrow fly?

1. Aug 4, 2015

Joe Collins

I have a PSE Drive LT compound bow. I would like to know how far my arrow will fly in optimal conditions. Here are the specifications. If additional information is needed feel free to ask.

Average arrow weight(in grains)- 358.030714
Draw length(in inches)- 26.5
Draw weight(in pounds)- 50
Arrow velocity when leaving the bow(in feet per second)- 253.32
Bow/projectile angle when leaving the bow(in degrees)- 45

Let's assume that barometric pressure is between 20-40 inHg, humidity is between 30-75%, 0mph wind, flat ground with no obstructions, 100 feet above sea level, with the temperature being between 50-80F.

The reason I want to know is because I'm curious as to what the limits of my bow are. Any help would be greatly appreciated. Thanks in advance!

-Joe

2. Aug 4, 2015

tommyxu3

You give the approximate barometric pressure and ask for the optimal conditions, so would you hope to calculate the situation with the resistance of the air?

3. Aug 4, 2015

Staff: Mentor

Welcome to the PF, Joe.

You can't neglect air resistance, especially because of the fletchings on the arrow. Figuring out the drag coefficient will probably be pretty complicated. It may be easier to just go out to an open field and test it yourself.

4. Aug 4, 2015

tommyxu3

It's really a practical good way, but the result may vary a lot to get an accurate answer? Maybe try to simplify the model?

5. Aug 4, 2015

Staff: Mentor

The results shouldn't vary that much. The OP should vary the launch angle a bit off of 45 degrees to find the optimum distance launch angle. With wind resistance, I think the launch angle will need to be a bit higher than 45 degrees to get maximum flight distance.

6. Aug 4, 2015

7. Aug 5, 2015

nasu

Any calculation will require to know the drag coefficient. Attempting to estimate this coefficient will very likely result in uncertainties that will be much larger than what you can get by direct experiment with your arrow.
I am not sure what even "a more accurate answer" will mean in this context. The range of your bow is not some constant, very "accurate" number. The best you can get is some estimate.

8. Aug 5, 2015

Joe Collins

I am looking for more of a range rather than a specific yardage; an estimate is what I'm after. I'm well aware that the arrow will not travel the same distance every time due to wind variations(which is why I omitted them), human error(differences in releasing the string, etc), and other factors. However, I do think the range of the arrow when fired at any specific angle will be relatively consistent. (i.e. If fired at 45.5degrees it will land between 500-520 yards consistently.) This is the type of answer I was looking for.

Unfortunately, I do not have a large piece of property in which I can fire my bow to test it's range. The guys over on the bow hunting forum suggested I do that, which is why I came here and asked.

9. Aug 5, 2015

nasu

So you mean you cannot actually use your bow to maximum range?
Why does it have to be your own property?
Sorry, these don't answer you question, just being curious.

But if want to compare bows, knowing the initial speed (which you seem to know) should be enough.
For same type or arrow, higher initial speed will produce longer range.

This may be interesting though:

It gives some specifics of some arrows, towards the bottom.

10. Aug 5, 2015

Staff: Mentor

The optimal angle is lower than 45 degrees. The arrow falls down steeper than it rises, making that even steeper does not help. The added range in the earlier flight increases distance more.

On the other hand, we usually overestimate angles relative to the ground, so aiming for 45 degrees or even more is probably not a bad idea.

Without an estimate for the drag coefficient of the arrow it is impossible to make reasonable estimates. Air resistance is certainly not negligible.

11. Aug 5, 2015

stedwards

You want someone that will happily solve your nonlinear differential equation for minimal action. This must have been done one thousand times, and is elemental in M1A1 target solutions. Ask the mathematicians. The physicists scratch their heads. The math guys should love this simple respite from whatever it is they do.