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Adjusting Airspeed for Altitude

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Marc W

Well-Known Member
Joined
Mar 31, 2017
Messages
1,234
Location
Colorado
I fly under light sport rules so anything I fly has to conform to LSA rules. My Thatcher CX4 has a claimed stall speed of 40 mph in the designers specs. It is to laugh! I have found the stall speed to be about 58 mph. This is however at 8000'. The practice area in my patch of sky is over a sloping mesa that has a cluster of private airfields. The lowest is at 6200' msl and the upper one is at 6800' msl. I normally do my testing at 8000' msl or so. Anyway, the question is am I legal?

LSA rules require the stall speed to be a max of 45 knots at sea level. This is about 51.8 mph. So my problem was to figure out what my stall speed would be at sea level if it is adjusted for altitude. I decided to use the lift equation since it depends on speed and density. My normal gross weight is 830 lb. so I used that for lift. I used the density values from the ICAO Standard Atmosphere and my 58 mph stall speed to solve for CL which turned out to be 1.557. I then used the CL and the density values for sea level to solve for speed at sea level. I came up with a stall speed of 51 point something mph which I didn't write down. This is a long way around but it was a good way for me to start given my rusty math skills.

I then worked on simplifying the process. My original solution required two equations. Both equations contain lift, CL and wing area. These are the same in both equations so they drop out. Density is the only remaining variable when the lift equations are simplified. I won't go through the whole process because it led to a really simple solution.

I came across the term density ratio a couple of times in my reading on this problem. Density ratio, sigma, is the density at any given altitude divided by the density at sea level. It is given in the Standard Atmosphere table I used. I played around with it a bit. Speed, or V, in aero speak is a squared term in the lift equation. Ergo, to find the speed at sea level corresponding to the speed at 8000', you take the square root of the density ratio at 8000' and multiply it times the speed at 8000'. In my case, the density ratio is 0.7860 and the speed is 58 mph. Equivalent speed at sea level is 51.4 mph, which is under 51.8 mph so I am legal!

You would have to use density altitude to be more accurate. However, in my case the solution is conservative. Standard temperature at 8000' is 30 degrees F. It was warmer than that when I did my stall testing so my density altitude would have been higher and consequently the stall speed at sea level would be lower. The Standard atmosphere is below. I think this is correct. Maybe Billski or somebody else smarter than me can verify.

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