Theoretical max rpm for a prop

[earthsciteach]

Check my math here, folks. I started off thinking about a really high rpm motor capable of swinging a 8 to 10" prop. I know that a prop can't exceed the speed of sound or bad things happen. Well, a prop CAN exceed the speed of sound, but its efficiency falls off a cliff and the noise level sky rockets.

I remember being at an EAA Fly-in in Kerville, TX back in the late '80s. Burt Rutan was giving a presentation on the future of air traffic control. About 5 minutes into his presentation (which was in a large tent), this guy starts performing his routine: http://www.youtube.com/watch?v=i6W-UzGUJ-A

Now, it is a beautiful airplane and he puts on a good show, but that 500 hp engine swings a 10' prop, of which the outer too much of the prop goes supersonic. The audio of the clip does not do it justice. If you want the first hand experience, connect your computer to a very large amp, turn the volume to full and place your ear directly against the speaker. It is painful.

Needless to say, Burt and everyone inside the tent were very annoyed.

To the math part... The speed of sound at sea level and standard atm pressure and temp is 761.1 mph. This converts to 13,395.6 in/s. As an example, let's determine the rpm's for a 6" dia prop at the speed of sound. Rotational velocity (in revs/s) = 13,295.6 in/s/3" (3"=radius of prop) = 4,465.2 rev/s or 267,912 rev/min.

w=v/r where w=angular velocity. Did I miss something with degrees vs radians, here? Its been way too long...

 

[colorex]

Uhhh I did it differently and found max RPM for 6" = 42660 RPM - 3850kv motor on 3S.

My method:

The prop tip travels 18.84 inches in one revolution (6" x pie).

And google conversion tells me, the max speed of a prop is: 803721.6 inches per minute

So dividing that distance into the distance of each revolution, we obtain the revolutions needed to travel that distance in one minute:

803721.6 / 18.84 = 42660.38 Speed of sound RPM for a 6" prop.

 

[Tritium]

Teach, teach, teach..............Math on a Sunday...........I don't THINK SO!

Thurmond

 

[earthsciteach]

I know, Thurmond. What was I thinking?

 

[bicyclemonkey]

... About 5 minutes into his presentation (which was in a large tent), this guy starts performing his routine: http://www.youtube.com/watch?v=i6W-UzGUJ-A

The Younkin's are from my town. Matt, the son flies RC at our club and Jim Younkin, Matt's Grandpa landed his full size cub on our club runway during a fly-in. Here's Matt taking my family for a ride in a Stinson Junior. Matt let me fly it for a while, it was a blast!

Sorry to steal your thread but I had to mention.

 

[lonewolf7717]

sometimes i suspect Teach already knows the answers to the questions he's asking. perhaps just trying to elevate the convo a bit....get away from the "how do i know my servos are plugged in backwards" type of stuff.

 

[Craftydan]

sometimes i suspect Teach already knows the answers to the questions he's asking. perhaps just trying to elevate the convo a bit....get away from the "how do i know my servos are plugged in backwards" type of stuff.

Wait, what? there's a way to tell that? even with JR leads?!?!?

 

[colorex]

Do I have to wait for tomorrow to get my mathematical opinion validated?

 

[lonewolf7717]

Do I have to wait for tomorrow to get my mathematical opinion validated?

You sir are validated! The math part I'm sorta iffy on.

 

[jetpackninja]

You know, I was doing fine until I got to the part with all the numbers, it all kinda just runs together after that for me

 

[tramsgar]

Mush, teach, mush! For each revolution the tip travels 2πr. At 3000 rpm the tip travels 2*(3000/60)πr/s = 100πr/s. If the prop is 1 m across, the radius is 0.5 m and thus the tip would travel 50π m/s ~= 157 m/s. The speed of sound at pleasant 20°C is 343.4 m/s. So the equation to determine at what rpm and prop size the tip speed matches the speed of sound is (rpm/60)*2*πr = 343.4. (To get the result in Mach is an exercise for the reader.)

Of course, I am most probably wrong as I suck at maths, and also just looking at the tip speed is not very rewarding as it disregards all aerodynamics, but at least I use SI units, wink nudge =).

 

[vk2dxn]

Stir the pot Pat...

I may be really off track with this one but back to the original question of max theoretical rpm of a prop would depend on the material that it is made out of and mass of the prop.
From what I understand that Jet turbines spin in excess of the speed of sound because they are ballanced and the material and weight of the spinning mass does not exceed the mechanical breaking point. Now as for the math to calculate that I honestly have no idea.

 

[Craftydan]

Stir away vk2dxn!

Pat, he's right -- material and the part's designs are stronger limits.

All MAS props spec to: max rpm = 16500/diameter(in inches)

APC has nearly a half dozen:
Glow - 190000/d
thin electric & folding - 145000/d
multirotor - 105000/d
sf - 65000/d
racing - 225000/d


Most other prop MFRs I've seen aren't posting RPM specs (I'm not sure they care to know). I know I've exceeded GWS's and HK's no-name-super-cheap-prop's max more than once. There are also a few makers that thrive on power setups pushing that blade over the sound barrier -- while it may be less efficient, it doesn't mean it won't produce even more thrust, just that the battery drain increases more than the thrust increases.

It's not the speed of sound that gets you, it's prop flutter as the blade flattens out.

 

[rcspaceflight]

Fun Fact: The "crack" of a bull whip is caused by the tip breaking the sound barrier.

 

[tramsgar]

Fun Fact: The "crack" of a bull whip is caused by the tip breaking the sound barrier.

True, and also the cause of the smacking sound when you win a slap-contest. As the hand approaches the cheek the air in between get infinitely compressed and thus reach supersonic compression.

Most other prop MFRs I've seen aren't posting RPM specs (I'm not sure they care to know).

It should be printed on every prop along with its size, mandated by RC law or something. Like the max pressure printed on tires.

 

[earthsciteach]

The Younkin's are from my town. Matt, the son flies RC at our club and Jim Younkin, Matt's Grandpa landed his full size cub on our club runway during a fly-in. Here's Matt taking my family for a ride in a Stinson Junior. Matt let me fly it for a while, it was a blast!

Sorry to steal your thread but I had to mention.

That's REALLY cool, BM!!!

 

[earthsciteach]

Uhhh I did it differently and found max RPM for 6" = 42660 RPM - 3850kv motor on 3S.

My method:

The prop tip travels 18.84 inches in one revolution (6" x pie).



And google conversion tells me, the max speed of a prop is: 803721.6 inches per minute

So dividing that distance into the distance of each revolution, we obtain the revolutions needed to travel that distance in one minute:

803721.6 / 18.84 = 42660.38 Speed of sound RPM for a 6" prop.

I think you are correct. I left out the fact that angular velcoity = 2 PI f, where f is the frequency in rev/s. In the end, I get 42,639.5 rpm.

 

[earthsciteach]

Stir the pot Pat...

I may be really off track with this one but back to the original question of max theoretical rpm of a prop would depend on the material that it is made out of and mass of the prop.
From what I understand that Jet turbines spin in excess of the speed of sound because they are ballanced and the material and weight of the spinning mass does not exceed the mechanical breaking point. Now as for the math to calculate that I honestly have no idea.

Certainly the strength of the material may be the limiting factor before the speed of sound is reached.. I was just curious at to where the rpms of a prop cause the tip to reach the speed of sound.

Props can exceed the speed of sound, but the drag increases dramatically, due to compressibility, as the prop reaches the speed of sound. This makes a super sonic airplane with a "standard" prop impractical.

 

[earthsciteach]

sometimes i suspect Teach already knows the answers to the questions he's asking. perhaps just trying to elevate the convo a bit....get away from the "how do i know my servos are plugged in backwards" type of stuff.

I'm honestly not that well thought out. LOL!

 

[rcspaceflight]

For absolutely no reason I want to build a machine that has a part spin faster than the sound barrier. It would be a completely useless noise maker. But what a noise maker it would be. It might be a nice side show piece if I ever make it as a musician.