The drag is significantly more for a windmilling propeller.
Both aerodynamic drag and energy lost in the engine contribute. I estimate you will sink at least 200 FPM faster if you let the prop windmill.
For aerodynamic drag, it's impossible to convert this into a feet per minute estimate because it varies so much with the design of the propeller and the overall drag of the airplane. But you can see here:
Aerodynamics for Naval Aviators, 1965
(page 149 in the page numbers, or 167 in the PDF) that the drag can increase significantly.
A typical fixed-pitch prop has a pitch of around 15 degrees (more details at bottom). A constant-speed prop which has lost oil pressure, and is not automatically feathering, is probably more like 5 degrees. (Feathering props are used on multi-engine planes to reduce drag if one engine fails. Non-feathering props are used on single-engine planes so if the pitch control fails but the engine still works, you don't lose all your power). Overall, the actual propeller parasitic (simple aerodynamic) drag increases by up to a factor of 3. Not orders of magnitude, but it's significant. Since there's no way for me to estimate how much of the total drag is due to the propeller, all I can say is that this is probably noticeable. However, if you have a cruise prop, or an adjustable prop set to high pitch, it's possible that it works out close to even, as above 22 degrees, the windmilling prop actually has less drag.
But then there's the extra factor of the drag created by the engine, which is probably much more significant. It's possible to come up with a reasonable ballpark figure. Estimation and highschool physics are required.
An airplane without power loses potential energy, in the form of altitude, to drag. Since the airplane's speed doesn't change, its kinetic energy doesn't either and only potential energy need be considered. We calculate how quickly energy is drained out of the airplane by the spinning engine.
Work is the amount of energy that is transferred from one place to another, and power is the amount of work over time. The formula for work (in a rotational system, such as an engine) is torque * theta, where theta is the total angular distance rotated. Power (watts) is expressed in joules per second, although here I'll figure power in joules/minute because our other time units are also in minutes. The joule, of course, is the unit of both work and energy.
Assume an airplane weighing 1000kg flying at 1500 meters AGL. Its potential energy is:
1000 kg * 1500 meters * 9.8 (gravity) = 14,700,000 J (14.7 mJ)
Assuming a propeller windmilling at 200 RPM, the angular velocity is:
2pi radians / revolution * 200 revolutions / minute = ~1260 radians / minute
I estimate the torque, given in newton-meters, is somewhere between 50 and 500 Nm, tending toward the high side. 50 is from my personal experience turning a propeller at slow speeds by hand, it's about that much force; but in the air I think this is extremely optimistic. 500 is a higher estimate, justified as follows.
Single-engine planes such as the Cessna 172 frequently have a 180HP engine. The propeller normally has enough air-grabbing ability to transfer that 180HP into the air at engine redline of ~2700 RPM.
Converting HP to joules / minute (1 watt = 1 joule/second):
180 HP * (746 watts / HP) * (60 seconds / minute) = 8057 kJ / minute
Assuming the propeller efficiency is relatively constant with RPM, you can convert propeller power delivery capability linearly with RPM:
8057 kJ / minute * (200 RPM / 2700 RPM) = 596 kJ / minute
So the propeller should be able to transfer about 600 kJ / minute back into the engine. This is in the ballpark of my estimate of 500. However, as not all the normal engine power goes into the propeller (due to mechanical losses and engine powered accessories) the estimate of 500 seems to be pretty close, and I'm sticking with it for sake of simpler math. This estimate is pretty seat of the pants - lots of error sources, like variations in propeller efficiency with RPM and being driven in reverse - are ignored. But if the propeller is less efficient, it dissipates more power - so even my high estimate might be too low.
Back to the engine failure. The power dissipated by the engine is therefore:
1260 * (50 to 500 or you pick) = 63 kJ to 630 kJ per minute
A Cessna 152 has a sink rate of 725 fpm when flying at best glide with stopped propeller (best glide speeds are normally specified with stopped prop); The Cessna 172 is closer to the mass I am using, and has similar glide performance, so I'll just use that same number. This is an estimated calculation, anyway. At 725 fpm descent rate (221 meters per minute) it normally takes 6.78 minutes to bleed off that 1500 meters of altitude you started with. Dividing potential energy by time:
14,700,000 / 6.78 = 2.168 MJ/min energy loss
At the low estimate (probably reasonable only for an engine that suffered total compression loss but no other damage), losing an additional 63 kJ/min only increases your sink rate by
(2.168 + .063) / 2.168 = 1.029
about 3%, or from 725 fpm to 746 fpm. You might not even notice this on the instruments, although if you snag on a power line at the last second as a result, you'll certainly notice that. However, at the high estimate, losing an additional 630 kJ/min would increase your sink rate by:
(2.168 + .630) / 2.168 = 1.29
29%, or from 725 fpm to 935 fpm. That's very significant. And this does not even include the extra aerodynamic drag from the spinning prop. It is only due to the energy lost in the engine.
So, in conclusion: If power fails, stop the prop.
There is, however, one final point. If you lost power because of a mechanical failure, it's very possible that the propeller will stop all on its own due to whatever damage caused the power loss. However, running out of fuel is the most common cause of in-flight power loss. If you run out of fuel, the prop will probably keep spinning unless you stop it yourself.
- Pitch angle in degrees is different from the way pitch is normally described, which is measured in inches, where something like 76"x60" would be typical. You can calculate pitch angle based on the propeller measurements in inches using the formula for helix angle. If you do, remember propeller pitch is specified at 75% of the diameter of the blade, rather than 100% as in the math textbooks).