What is the max RPM any propeller can spin before it becomes useless?

Hi, I am new to boat design and really the science behind boating. I heard somewhere that on airplanes there is a certain RPM at which the propeller no longer creates thrust whether this is true or not I am not sure. If this is true I am wondering if there is some similar property on boat props.
I know about cavitation but I also know or assume that racing boat props are turning at very high RPMs so how to they avoid cavitation that degrades their thrust.
I am asking this because I want to see if I can drop a 4 speed transmission down in a inboard diesel boat and have it work properly having all the gear ratios correct of course. I am curious if this transmission with the gear ratios being lower in first and second if this would allow me to run a larger prop. Just questions and thoughts again I am very new to this so I could be completely wrong.

 

First of all, welcome to the forum.
Next, the questions you want answered (not asked) are all situationally dependent, and will be difficult to answer in a limited format such as this forum. Realistically, it would take a complete propeller design course to answer them all. So rather than just send you off and tell you to learn prop design. I'll hit the major points behind you questions.

Ok, there are five things this that define propeller performance at any given time; pitch (P), diameter (D), rpm (n), speed of advance (Va), and blade area ratio (BAR). Propeller blade geometry is determined by the pitch ratio (P/D) and the BAR. (NOTE: Most modern aircraft and some ships have controllable pitch propellers. This means that the root pitch, but not blade geometry, can be varied some amount from a most efficient setting. At this most efficient setting they are effective fixed pitch propellers of the same geometric P/D. To keep this simple we will only discuss fixed pitch propellers because a controllable pitch propeller is just a poorly designed fixed pitch propeller at some other pitch ratio) Pitch ratios run from about 0.5 to 1.4, giving rise to dimensionless families of propellers of arbitrary D and BAR, but different P/D with corresponding thrust (T), torque (Q), and efficiency as shown below.

Now getting back to your question: is there a rpm (n) where there is no thrust? The answer is yes, but it depends on the speed of advance (Va) and the diameter (D). Note that the lower axis in the above figure is Advance Coefficient (J) J=Va/(nD). So in the above figure for a P/D =1.0, notice that the efficiency and the thrust coefficient (KT) go to zero at about J= 1.06; so therefore any combination of Va, n, and D which results in a J above 1.06 would give no thrust.

Actually, there are propellers designed to operate while cavitating. See my two posts below, especially the figure in the first.
What is world's biggest planning hull boat and how fast? https://www.boatdesign.net/threads/what-is-worlds-biggest-planning-hull-boat-and-how-fast.64476/page-6#post-898807
Prop pockets and surface-piercing propellers https://www.boatdesign.net/threads/prop-pockets-and-surface-piercing-propellers.65196/#post-901746

Yes, it could work, but you would need to be very careful or you will blow up the engines. Notice the torque (Q) required (via the torque coefficient, KQ) in the graph above. As J increases, KQ drops. At a constant throttle setting, as the vessel sped up, the engine would start to run away. See my discussion in the thread below.
Oversized prop compromise https://www.boatdesign.net/threads/oversized-prop-compromise.64505/#post-888107

 

The OP probably needed to give more detail about what the intended end result is, the limitations are likely to elsewhere than the propeller.

 

Jehardiman thanks for such a detailed response I'm sorry for the lack of detailed information as I really have no idea about propellers. Thanks again.

 

The OP might want to purchase a copy of Dave Gerrs Propeller Handbook.
It explains the technical aspects in easy to understand language.

 

There's not really a top speed. Look at a top fuel drag boat. 260 mph in 3 seconds. Prop is turning faster than 20000 rpm. No circulation occurring, strictly getting thrust from the pressure side of the blades.

 

There's not really a top speed with aircraft propellers either, as such. Instead what happens is the tips of the prop blades approach and then pass the speed of sound. The nature of the flow around them changes in character, and the blade form that worked very well below the speed of sound doesn't work well at all. It is totally possible to make an airfoil that works above the speed of sound, but no one bothers, because jets work better.

 

While it is true that a propeller driven boat or airplane will only go as fast as the EPH you can deliver to it, in the actual physical working of a propeller there is a given combination of Va, P, and n where no thrust will be developed. P x n is called the geometric advance. In order to produce thrust, even with a cleaver prop, geometric advance must be greater that Va: i.e. there must be "slip". This is the point where the AoA of the blade sections is not producing any axial drive.
When we think of propeller "thrust", we think of what is called the "first quadrant" i.e. n+ and Va+. There are 3 others (in order CW from the first); crash ahead (n+ and Va-), astern (n- and Va-), and crash back (n- and Va+). Each of the quadrants correspond to the 4 90 degree quadrants of AoA on the blade, i.e. the AoA can physically go from 0 to 360). In each of the quadrants there are areas where is no "thrust" as we think of it, but areas where power is actually being put into the prop (i.e. the areas where hydro-generators and wind turbines work). These are areas were extreme caution is required because you can break the props or in aircraft (such as in a steep dive) you can overspeed the engine. FWIW, most aircraft and wind generator tips can travel faster than the speed of sound, which is why they make that noise, but generally they are not operated that way due to vibration fatigue issues similar to hydrodynamic cavitation issues.

 

You are generous with your time sir.

The OP asked about a max rpm though.