The quote mentioned tip mach number referring to aircraft props and cavitation referring to boat props. It was a general discussion that was about both aircraft and boats. Yup, cavitation is a liquid phenomenon.

Not sure about jets but ducted fans have higher thrust when on the ground. The difference is that they generally have less thrust on the ground than a prop, but more thrust than a prop at speed, but they still have more thrust on the ground than when in the air. F=MA is still at work, the air is accelerated to a higher delta V when on the ground which is more mass to create the higher thrust on the ground. F=MA is easier to calulate with fans and jets because almost all of the air goes straight back. With a prop some of it goes to the side near the tips, and some wraps around in a vortice at the tip, some is lost against the cowl, and some is lost with frictional losses against the fuse.

No calculations are really needed - jets are reaction devices
inlet air is heated and accelerated.
Fan jets are props running at extremely high pitch and speed -which also produces a fast flow - but soon, the drag exceds the thrust -even tho the theoretical prop speeds are much higher.
Neither increase thrust as the craft increases in speed.
As altitude increases, prop efficiency decreases and reaction engine efficiency increases
In zero atmosphere - even a tiny reaction device will continue to accelerate the vehicle ( (ion drive as an example)

Actually the propulsive efficiency of both increases with altitude. The turbine engine is also more efficient at altitude, and the aircraft has less friction and thrust is down it is also easier to push the plane and total propulsive efficiency goes down. With a piston engine the efficiency stays about the same or drops slightly though the prop eficiency goes down the total effect is not that great, thus because the airplane has less friction at altitude it also uses less fuel and greater speed at altitude though not as dramatic as a jet turbine. This is especially true if the engine is supercharged.

- My point was that as the air really thins out you simply have nothing to move.
a reaction engine works better and a rocket really comes into it's own. I have run into discussions where some modelers believe that rpm readings on a given engine improve at higher altitudes .
If you persue this argument - you have a condition where the prop goes fastest as the engine looses all power. In real world the engine loses and the prop working in thinner air gives fairly close readings for the same setups.
The hooker tho is that the aircraft must go faster to produce the same lift. and the engine is producing less power
If you fly an aerobatic model (contest type stuff)
at 7000 ft elevation and at sea level- the results are extremely different
You have to readjust and compensate for speed variance.
Just like a car at sea level and when going over the contenental divide.
Less air resistance up high but no power to move the car.

Yes but because of the thinner air there is less drag and going faster only helps with the effeciency. Also it is suprising how little power a jet engine or even a supercharged piston engine loses at altitude. This simulator can demonstrate that.

http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html

I am familiar with supercharged engines - I ran a GMC blower -on the street .that was many years ago
anyway, ANY given engine (IC) at sea level will loose power at altitude - any of em. It takes power to drive a supercharger
The higher you go - the more you must pump pressure and the NET power eventually becomes zero.
Basically:
props are best in thick air
jets better in thin air
and rockets best with no air.
3 blades 2 blades 6 blades
each has it's place.
My cheezy test stand using an electric motor and measuring watts used and readng prop thrust , shows that very clearly.

Actually, supercharged piston engines do loose power significantly, once past 'rated altitude'. With any boosted power system the throttle opening is limited by the induction pressure, the cylinder strength, if you like. As density decreases, the throttle can be opened, until, at 'rated altitude' it is wide open. After that the engine loses power as it climbs. The limits were reached back in the mid '40's, around 50,000 feet and 500 mph indicated. Gas turbines, conversely, will always pump just what they need, so long as there is air to pump. They do increase thrust as their speed increases, due to both ram effect and the lower air temps allowing more fuel to be burnt as they climb. At 50,000 feet turbines are limited by the skin temps of the aircraft carrying them, not the lower density of the air. So there are huge differences in the operation of the two propulsion systems. Propellers are very efficient, up to 300 odd mph, after that a turbine will be favoured. Take a look at your local airport and you will see very clearly the sort of division I mean.
Evan, WB #12.

Yes, but with large engines that rated altitude could be very high, and many do loose a small amount of power up to rated altitude for the reason Mr. Dick Hanson mentioned.