Calculating Power Required
Mar 28, 2008  Section IV
Theory & Understanding, Aerodynamics
A question came up as to which wing will require more power to stay
up. I'm not concerned with covering miles, just staying airborne. First,
to stay up the longest on any given wing, fly at the speed that gives
the lowest sink rate when power off. For paragliders, that's usually
slow trim, no speedbar and brake pressure between 1 and 2 (about the weight of your arms) but
do with what the manual says.
How about comparing wings, though? There are many variables, but
here's one way to look at it. Thanks to Dana Hague for contributing this
morsel.
For any given airspeed, power required for level flight
equals sink rate times all up weight. You must have enough power to
overcome the sink and fly level. That's the same as excess power
required to climb at that rate. So if you're sinking at 300 feet
per minute, the power required will be the same as the excess power
required to climb at 300 feet per minute.
For actual numbers the units must match. We'll use the ridiculous
English units we're (unfortunately) most familiar with: sink rate in feet per second
(ft/s) and power in lbft/s. One hp = 550 lbft/s.
Lets take a 250 pound PPG (all up weight) that sinks at 300 feet per
minute or 5 ft/s. You would need 250 lbs x 5 ft/s or 1250 lbft/s of power
required for level flight—2.27hp. If that sounds absurdly low, remember
our props have maybe about 30% efficiency so the motor would need to be
7.5hp. Again, that's just to maintain level flight. Now figure you want
300fpm climb; that doubles the power required to 15hp which is typical.
We can also use this to figure thrust since power equals thrust times
velocity. Assuming 30 ft/sec (20.5mph), 1250/30 = 41.7 lbs thrust for
level flight or 84 lbs of thrust for 300fpm climb. Again, these numbers
seem low, but that could be (1) a reflection of thrust dropoff
from a prop optimized for static thrust, 2) the effects of "dirty air"
(turbulence) behind the pilot, or 3) manufacturer's overly optimistic
claims.
Another observation you can safely make from this discussion is that
larger wings, having a lower poweroff sink rate, will require less
power to remain aloft given the same efficiency.
Glide Ratio and Covering Miles
Now if your mission is to go somewhere than look for a good glide
ratio a.k.a. lift/drag ratio. A glider with a high glide ratio will go
farther on less fuel than one with lower glide ratio regardless of its
sink rate. After all, you can fly a large wing to get a low sink rate
but you'll be snail slow trying to get somewhere with it.
Here is further discussion on weight,
speed and glide ratio.
