Thrust factors

[zul8tr]

In theory, what effect would a one inch decrease in diameter have on thrust, in conjunction with the RPM increase that would be produced, by a propeller moving through the water, if no other factors were changed?
(This is an example to make understanding what I'm asking more understandable. These numbers are for simplicity and clarity only). For instance, if I had a 10 inch prop producing 100% thrust at a given RPM and NO other factors changed (horsepower, pitch, blade shape, style, or number, drag, viscosity, velocity, etc.), and I reduced the diameter 1 inch, the thrust would be 90% at the same RPM, then 80% for 2 inches, 70% for 3 inches....
Now, the question again in its final form. Using the above example: What would the thrust be with the increase in RPM? Would the thrust be less than 10% decrease or more than 10%, for each 1 inch diameter decrease?
I'm not interested in the effects hull design have on the equation. I'm just talking about a prop moving through the water. Blade shape, design, and number, exact figures or Reynolds numbers are irrelevant in this question. I'm aware that these factors all have an effect in reality, but I am not interested in these effects for this theoretical question.
Ken

From a pure theoretical aspect the thrust provided by a propellor pushing a fluid (water or air) per the momentum theory is related to

Thrust = mass flow rate thru propellor x Velocity

More specifically the variables are: density of the fluid, the area of the propellor disk and the square of the change in velocity (acceleration) of the fluid thru the propellor or:

Thrust = Ct x ro x area x (Vj^2 -V^2)

Ct = thrust coefficient, via experiment
ro = density, esentially constant for water but very variable for air
Vj = velocity of water jet exiting the prop i.e the water we see going
backwards from the prop. Note low roostertails = more thrust

V = velocity of boat, opposite Vj

Since area = pi/4 x D^2

D = diameter

Then

Thrust = Ct x ro x pi/4 x D^2 x (Vj^2 -V^2)

Note V and Vj are related to propellor rpm = engine rpm/ gear ratio
Also note that the thrust is a max when the boat is not moving or pushing at max rpm and not going forward. Also as the boat speed increases the thrust decreases and at max speed the thrust is exactly equal to all the drag.

Thrust is very sensitve to diameter and velocity change since they are related as the square. Thus if all else remains the same and the diameter was decreased by say 1" on a 10" prop that would result in a relative thrust change of (9/10)^2 = 0.81 or a 19% reduction. However this assumes that there is no change in Vj and V the velocity change thru the prop and for a diameter reduction there would be changes in the velocity thru the prop.

There are many variables and thus the analysis is quite complex especially when surface piercing propellors are considered.

Here is an interesting analysis I found for a jet ski. The same principles apply in that the water jet moving backward is an anology to the prop moving the water backward.

http://greenhulk.net/forums/showthre...=thrust+output

Here is a text by Dave Greer on propellors that has some usefull insight

http://books.google.com/books?id=8w0...snum=9#PPP1,M1