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 lb-ft/s. One hp = 550 lb-ft/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 lb-ft/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 power-off 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.