Simple steady-state climb equation
Hey Bill,
Like Kyle pointed out, an airplane climbs on excess power. We define "excess power" as the power available in excess of that required to maintain steady-state flight (level, 1g, unaccelerated condition).
Keep in mind that we're talking about
power here, not force. Power is equivalent to moving a force through a distance in a certain amount of time. For an airplane climbing, this is equivalent to:
Excess thrust (TE): thrust above that req'd for steady state (pounds)
Force moved (W): The airplane's weight (pounds)
Distance: Altitude gained (feet)
Time: Time during the climb (seconds)
The hardest part of this problem to solve is knowing how much excess thrust you have on hand. Best way I know to get this is by test flying your airplane and taking down some data.
Fly a data point at a steady state that's just below your cruise speed. Record the speed (TAS), your GW (lbs) and RPM and MAP since we need to know how much crank HP you're making at that point.
Now go to your climb power, and hold the airspeed steady. Record the climb rate (fpm), the MAP and RPM.
We need to back out your excess thrust from this data. Here's how to do that. The basic equation for steady state climb looks like this (for small climb angles where the tangent of the angle is small, less than 3 degrees or so):
Climb rate (feet/second) = [excess thrust (lb) x true airspeed (ft/sec)] / weight (lb)
Solving for TE:
TE = Rate x W / TAS
We need to keep consistent units, so remember to convert your TAS to feet per second and climb rate to feet per second also.
You now have TE (excess thrust in pounds) for that data point. If you want to factor in propeller efficiency, for a good prop it will be close to .85. For a not so good prop, maybe .80. The prop efficiency is basically the difference between "crankshaft thrust" and "propeller thrust".
If you want to know actual excess power, in HP, then you need to convert units again. Since one HP is defined as 550 ft-lb/sec, take your excess thrust, divide by 550 and then multiply by your climb rate in fps. The result will be excess horsepower (propeller horsepower, not crank HP).
Take several data points like the one above. Develop a database of your airplane's performance. Now you can goof around with answering your original question: "If I install more HP, but weigh more, how will it affect performance?"
Keeping all other factors equal, and just changing TE and weight you can solve for the new climb rate, using the basic climb equation.
And, if you like, just go fly and take the data like I said. Send it to me and I'll be happy to work up a spread sheet for you. I used to do performance analysis for General Dynamics. But this will cost you a ride in the plane some day
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