A question that has come up from time to time (and one that affects me through a product review that I am currently working on) is if altitude changes affect arrow flight. If it does, what should be done to compensate for it?
Air pressure and density are largely a function of altitude. At sea level and 70 degrees Fahrenheit the average air pressure is 14.7 psi (101.4 kPa) Where I live in Colorado, at around 5000′ altitude, the pressure is on average 12.2 psi (84.12 kPa). To go even more extreme, I often hunt elk and mule deer at around 10,000′ altitude where the pressure is 10.1 psi (69.64 kPa). Air density is directly related to the air pressure; as the pressure rises, the air particles are packed closer together thus increasing the density of the air. For altitudes of 0′, 5,000′ and 10,000′ the air density is .0766, .0660 and .0565 lbs/ft.^3 respectively.
It is the density that is of primary concern because the drag that air exerts on a moving object is directly related to the density of the air:
Drag Force = 1/2*density*v^2*A*CD
Where density is the density of air, v is the speed of the arrow, A is a function of the cross-sectional area of the arrow and CD is the coefficient of drag. As the density of air goes down, so does the drag on the arrow. A certain famous gentleman by the name of Sir Isaac Newton also tells us that the force on a object is proportional to the objects mass times it’s acceleration:
F=m*a
In this case, F is equivalent to the drag force on the arrow that is decelerating the arrow. Relating both equations together shows that as the air density rises, so does the deceleration of the arrow. Shooting an arrow where I live will experience over 16% less drag force than an arrow shot at seal level. Up at elk camp, the difference is over 35%. That can be quite a difference and can make a noticeable change in sight pin spacing. When translated into actual arrow drop over distance, it is not a huge difference, but it is measurable and warrants paying attention to if you change altitudes significantly with your archery equipment.
It’s exactly the same phenomena that makes Coors Field, home of the Colorado Rockies baseball team, the home run capitol of MLB. Because the air density is lower, the baseball decelerates slower and it is easier to hit the ball out of the park. Sea-level golfers also love coming to Colorado and watching their drives soar further down the fairway.
If you travel with your bow and have a significant change in altitude from your starting point to final destination, it is worth taking the time to shoot the bow at all distances that the sight is set for (this should be done anyhow in case anything gets bumped or vibrated out of position). Will there be drastic changes that could make you miss the trophy of a lifetime? Most likely not, but on a marginal hit every inch can count. If you are shooting a 3D tournament it could easily cause you to miss the 12 ring at 40 yards. It will also change your arrow speed enough that if you are attending an ASA (or similar) event that it could put you over the 280 fps speed limit if you are borderline to begin with.
Someday when I’m feeling a little more aggressive and have the time, I’ll run the numbers and throw up some charts.
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Hello I am Portuguese Champion 3D, where the altitudes are practically at sea level. I’m preparing for the European 3D will be estimated at an altitude of over 2,000 meters (+-2500m). I wonder if there is actually a formula that I can approach the reality of power and speed at that altitude in relaçãoao level of evil (where I am).
Thanks in advance! (even with years of exprience never know everything, without going through real situations.)
Luís, you could actually run all the calculations on the fluid dynamics and vary the density/humidity of the air, but the would be a lot more work than getting to your intended shooting altitude and checking your pins. Unfortunately there are a lot of variables that go into the calculations and it’s not an easy thing to do on paper!