So much from so little...Prop Physics?

Please help me to understand something-
How can increasing the prop rpm from 2500 to 2700 rpm (fixed-pitch) generate a few knots of speed increase? If I were sitting on the ground and could idle the engine at 200 rpm, there wouldn't be enough thrust to get her rolling. How does this work?
Don

A simple explanation could be thought of by looking at the extremes.
If your prop were running at 1rpm, it would not pull much. If your prop were running at 10,000 rum, it would pull like crazy.

Rather than looking at whether or not you can move it at 200rpm, look at the difference in movement from 1000 to 1200 rpm when taxiing. You can see the pull is stronger and you are going faster. Fixed pitch, direct drive, means the faster that prop is turning, the faster you go. The more times per minute you can whack the air with the prop, the more thrust you have.

Same thing is happening to you in the air and you should generally see faster speeds with increase in RPM.

Screw

Brits used to call them "Airscrews" as I recall. Since the prop acts as though it's threading its way through the air, the faster it turns, the faster it screws itself throught the air. Kinda like a nut and bolt, huh? Turn it faster and the nut moves the length of the bolt faster.... Boat props work the same way....A prop is assigned a pitch number and a diameter number. Mine is 66 X 72, meaning 66 inches in diameter and if there were no slippage, would move forward 72 inches for one revolution.....Thus, faster revolutions per minute would equal a greater distance travelled in that minute.

My .02c,

Mathematics

As I understood the original question, he was asking why the 200RPM difference is more significant at higher overall RPM settings (that is an increase of 200RPM starting from 0RPM isn't very significant, but an increase of 200RPM starting from 2500RPM is quite significant).

Here's an explanation of why this is true - it's just mathematics:

Power = k * P * D^4 * N^3 where:

Power is in Watts
P = prop pitch in feet
D = prop diameter in feet
N = RPM in thousands

The key is that power is a function of N^3 (not a linear function of N). Small changes in N starting from low values yield relatively small changes in power. But small changes in N starting from high values yield very large changes in power. Just draw a graph of y=x^3 to see this. The curve gets much steeper for higher values of x.

So when you increase N from 0 to 200 RPM, you increase the power by approximately
200^3 - 0 = 8x10^6.

When you increase N from 2500 to 2700 RPM, you increase the power by approximately
2700^3 - 2500^3 = 4x10^9.

4x10^9 is much bigger (500 times bigger) than 8x10^6.

(the "^" above is used to indicate an exponent. i.e. "x^y means "x to the power of y").

Intentionally running higher RPM

I think this question is appropriate for this thread.

I'm trying to study the idea of using a souped up o320 on my RV8 with a fixed pitch prop to save on weight. I've read somewhere on the forums a prop designer suggesting running the engines at higher rpm (2700-2900).

If you can get 2500 rpm on the ground roll, for best climb and whatever greater rpm that translates into at cruise and lower hp at altitude is this a good trade? I'm trying to understand how to get constant speed advantages without all that weight, AD's, expense, etc. I know in physics/engineering there are no free lunches, just want to understand what going on.

Concern with Mr. Kaye's reply

I have no argument with the cube factor - that the increase percentage in rpm will require a cubed percentage increase in power. The problem is that the airspeed is why that is true. It's about the parasite drag curve and so the question is not really answered.

If you ignore power, the airspeed is proportional to the RPM pretty much linearly in the range of RPM's at which we normally fly. Said another way, the effective pitch of the fixed pitch prop (example 73") does not vary much within that range. I've been keeping track of mine for other reasons, so I'm pretty confident of this observation.

I don't know why 200 rpm on the ground is not as effective as plus 200 in flight, but I agree that 1000 vs 1200 is a better analog. Maybe the first few hundred RPM are where the "slip" is experienced and the rest gets added? We know that slippage exists because 2400 rpm static vs 2400 in a climb vs 2400 in level flight all give a different result in airspeed.

hevansrv7a said:

I don't know why 200 rpm on the ground is not as effective as plus 200 in flight, but I agree that 1000 vs 1200 is a better analog. Maybe the first few hundred RPM are where the "slip" is experienced and the rest gets added? We know that slippage exists because 2400 rpm static vs 2400 in a climb vs 2400 in level flight all give a different result in airspeed.

Click to expand...

I think the difference is that at 200 rpm the aircraft is sitting still. You are looking a "break out force" required to move the aircraft. Once you "break out" of sitting still, rolling friction is much less. If the airplane was sitting on ice, I think 200 rpm WILL move it.

tinman said:

Please help me to understand something-
How can increasing the prop rpm from 2500 to 2700 rpm (fixed-pitch) generate a few knots of speed increase? If I were sitting on the ground and could idle the engine at 200 rpm, there wouldn't be enough thrust to get her rolling. How does this work?
Don

Click to expand...

there are 2 parts to this answer: 1) horsepower is not linear at the extreme ends of the power curve in piston engines 2) props are optimized for airspeed and rpm.

2700 rpm = 100%power = 180hp
2500 rpm = 92.5% power = 166hp
diff = 14hp = ~5 ktas

assuming a hypothetical linear power curve, at 200rpm the engine would make about 13hp (200/2700*180)

(in reality the engine might make 5hp if it could run that slow).

at such slow speeds, the prop is doing nothing because the blade profile is optimized for higher rotational and forward speeds.

at 200 rpm an RV prop has no traction. there are props that would "bite" at 200rpm but they are found on helicopters and Ospreys, i.e. very large diameter

large props are like glider wings....very efficient but very slow.
smaller props are like RV wings.....inefficient. they only generate lift at higher speeds.

there's an upper limit to "adding rpm". props become enormously inefficient as tip speeds approach mach 1 .... anything above .85mach will cause props to lose thrust regardless of how much power is applied. 2700 rpm is the upper limit for props in the 72-74inch range...tips begin to go supersonic = enormous drag.

case in point: some RV's are known to LOSE a few knots when increasing rpm from 2600 to 2700.....prop in this case is losing efficiency at 2700. all of the added power (and fuel) is lost to drag at the prop tips.

Our engines are basically operating where the torque is pretty much proportional to MAP, and for a given MAP, the torque is fairly flat over a range of several hundred rpm. Since power is torque times rpm over a constant, if your engine is capable of increasing the prop's rpm from 2500 to 2700, the power will increase by 1.08, 8%. If the prop is efficient over that range of rpm, you should expect to go 1.08^1/3 or about 1.026 times faster. If the prop is designed, for a given drag load, to deliver rated rpm at the highest density altitude to be flown, then at lower altitudes and take-off the rpm, and power, will be higher than if the prop is designed for rated rpm at, say, 75% power. This will give much better take-off and climb performance. My three-blade prop turns the O-235-rated 2800 rpm at 10,000' dalt and I go 201 mph TAS. At 1000' dalt, I turn 2950 rpm and go 214 mph TAS. Static rpm is 2210, and climb, at 110 mph IAS, is 2410 rpm, 1500 fpm at 1350 lb. The concept of a propeller having "slippage" is a not very scientific approach to propeller dynamics. As with a wing, as the load is varied, the propeller will assume different angles-of-attack. On my plane, the same static rpm of 2210 will yield 159 mph TAS in level flight. The only pitch that should be attributed to a propeller is the effective pitch obtained for a given plane's drag-power combination. On an efficient prop, that value changes very little with speed, and is computed by TAS, mph, times 1056 divided by rpm, with the result in inches. If your fixed-pitch prop does not have a consistent value vs speed-rpm, then it is not matched well to your airplane.