PPRuNe Forums - View Single Post - Angle of climb/rate of climb
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Old 24th Sep 2011, 21:16
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carldanner
 
Join Date: Sep 2011
Location: Bakersfield CA
Age: 77
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Maximum climb

The height in meters that any vehicle can climb is found by using this formula:

ENGINE POWER IN WATTS
times
POWER LOSS FRACTION AT THE VEHICLE'S SPEED
times
DISTANCE TO OBSTACLE IN METERS
divided by
VEHICLE WEIGHT IN KILOGRAMS
divided by 9.81 ( Earth GRAVITY FACTOR )

The formula indicates that climb distance will:
A. increase in proportion to engine power.
B. decrease as efficiency decreases.
C. decrease in proportion to vehicle weight.
D. decrease as gravity increases.

For and aircraft the efficiency includes:

A Propeller efficiency which is typically about .3

B aircraft lift efficiency this could be about .8
Aircraft lift efficiency normally decreases with speed due to increased drag at higher speeds but lift efficiency also decreases at lower speeds near the stall speed due to increased turbulence.

If the numbers above are used then the total aircraft efficiency would be .3 times .8 which is .24

One horse power is 745.7 watts.
One mile is 1609 meters
One pound is .45359 kilograms

The calculations indicate that there is a sweet speed for maximum climb distance to an obstacle that is somewhere above stall speed and below higher speeds. That speed is the speed where the aircraft efficiency fraction is highest. This will probably be the lowest speed where you sense that losses due to turbulence and drag are minimum.

This sweet speed should also give the maximum climb distance in a given time because the maximum power from the engine is being transferred into the task of climbing. As far as clearing an obstacle goes, I would error on the side of going slower as long as efficiency seems OK since the aircraft will have more time to expend energy climbing before in hits the obstacle. This will also give you more time to think about how to avoid the obstacle as well as the fact that you will be going more slowly should you hit the obstacle.

My credentials.
I took flying lessons many years ago and soloed in a Cessna 152 but I
am not a pilot. I was working on electric vehicle charging systems when I came across this discussion while doing vehicle climb rate calculations. You can check out my site at EVfueling.com but I have not spent much time working on the site in the past year or more because I am working on a fueling calculator spreadsheet that will help quantify factors related to vehicle fueling.

Have fun flying.

Carl Danner
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