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

[kenboyd]

zul8tr,
EXCELLENT!! You hit the nail on the head. Very interesting and informative read.
The links are great! They get very deep into related subjects. It looks like I'll have hours of stimulating insights, from all the information you provided through these links. Thanks Peter

[capnzee]

After you finish working all the numbers you may have to test, if for no other reason but to find out you wasted a lot of time you could have spent on the water having fun.

[zul8tr]

After you finish working all the numbers you may have to test, if for no other reason but to find out you wasted a lot of time you could have spent on the water having fun.

No doubt testing is the last word but understanding the principles (that he asked for) is definately a plus. If Edison better understood the principles he probably would have expended much less than 99% perspiration and had more than 1% inspiration for his inventions - he never should have fired Tesla.

[Smokin' Joe]

Gerr's book is well written for laymen, I'm reading it. Unfortunately, we do not really understand what goes on with surfacing props, except that they leave and reenter the water and behave like a rotating hydrofoil. From a basic standpoint an airplane wing, a prop blade and a sail all generate high lift(thrust)/drag by the same nonintuitive method: circulation is generated around the foil by shedding vorticity from the trailing edge. A too large angle of attack increases eddies shed at the leading edge, which only amounts to drag. The theory of propellers today is actually not better than it was 30 years ago, amounts only to scaling by various constants (Reynolds nr., Froude nr., etc), assuming that drag is some power of the dimensionless speed, then fixing coefficients empirically. That's what Gerr's book is about.

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

[zul8tr]

Gerr's book is well written for laymen, I'm reading it. Unfortunately, we do not really understand what goes on with surfacing props, except that they leave and reenter the water and behave like a rotating hydrofoil. From a basic standpoint an airplane wing, a prop blade and a sail all generate high lift(thrust)/drag by the same nonintuitive method: circulation is generated around the foil by shedding vorticity from the trailing edge. A too large angle of attack increases eddies shed at the leading edge, which only amounts to drag. The theory of propellers today is actually not better than it was 30 years ago, amounts only to scaling by various constants (Reynolds nr., Froude nr., etc), assuming that drag is some power of the dimensionless speed, then fixing coefficients empirically. That's what Gerr's book is about.

Agreed on what Gerr's book is about and I was only offering it to provide some basic info for prop theory and agreed that surfacing props are difficult to understand and predict performance. But I have found my rather simple relations have proved to be very useful in setting up my hydro.

As far as the lift/drag theory of wings, props and sails by nonintuitive I would add that for sails there is another theory out there. Since a sail is a thin cambered sheet when properly set in the wind there is no relative difference in cambered shape of the front and the back face like there is with a wing and prop blade. Therefore the usual wing theory of lift by pressure difference from the lower pressure on the greater curved side than the flatter does not totally apply to a sail. A more reasonable explaination results from the sail simply changes the direction of the air from the leading edge to trailing edge that passes around it and that deflection constitutes a force from Newton's F=ma. The angle that the air enters the sail is different than when it leaves at the trailing edge thus resulting in sail force. Therefore for sails the greater the deflection the greater the force (within limits of course). No doubt that shedding eddies has some contribution as well as other items. If interested here is a fairly good explaination of the theory:

Prelude
http://www.sailtheory.com/wrongtheory.html

Theory
http://www.sailtheory.com/sail.html

[Smokin' Joe]

Thanks for the communication. Regarding the link, the writer hasn't studied enough hydrodynamic theory. A flat plate at an angle to a fluid flow experiences both a lift and a drag, but without circulation about the plate you can't get an efficient lift/drag ratio (a boat bottom is indeed like a flat plate with an incompressible fluid on only the bottom side, neglecting the air flow over the top to first order). But an airplane wing can't lift off the ground like that. Another way to say it: if you neglect drag (vorticity creation), and so treat the fluid as ideal and then calculate the net force on the plate or sail then the net force vanishes vanishes (this is a standard theorem in hydrodynamics--if you throw a block of wood into a hypothetical idea flow then the river does not carry the block downstream). In a real, viscous fluid like air or water a sail can't work efficiently simply with wind blowing against it, the drag will match the thrust/lift. If you can get the circulation started around a mast with no sail, then the mast will experience a side force relative to the wind. I have to warn you that freshman and sophomore physics texts get this wrong, in reviewing those books in the past I railed against that mistake to no avail. But engineering texts do not get it wrong, nor do advanced physics texts on fluid mechanics (like Landau-Lif****z, e.g.).

Apparently, it would be necessary to spell Lif****z in Russian to get this name past the web control: Лифшиц

Agreed on what Gerr's book is about and I was only offering it to provide some basic info for prop theory and agreed that surfacing props are difficult to understand and predict performance. But I have found my rather simple relations have proved to be very useful in setting up my hydro.

As far as the lift/drag theory of wings, props and sails by nonintuitive I would add that for sails there is another theory out there. Since a sail is a thin cambered sheet when properly set in the wind there is no relative difference in cambered shape of the front and the back face like there is with a wing and prop blade. Therefore the usual wing theory of lift by pressure difference from the lower pressure on the greater curved side than the flatter does not totally apply to a sail. A more reasonable explaination results from the sail simply changes the direction of the air from the leading edge to trailing edge that passes around it and that deflection constitutes a force from Newton's F=ma. The angle that the air enters the sail is different than when it leaves at the trailing edge thus resulting in sail force. Therefore for sails the greater the deflection the greater the force (within limits of course). No doubt that shedding eddies has some contribution as well as other items. If interested here is a fairly good explaination of the theory:

Prelude
http://www.sailtheory.com/wrongtheory.html

Theory
http://www.sailtheory.com/sail.html

[Mark75H]

I have read that advanced research always presents angle of attack as the strongest force in lift.

Going thinner and increasing angle of attack increases lift, which is contrary to "airfoil" lift theory. A wing has lift if it has angle of attack, regardless of how thin it is.

[Smokin' Joe]

When the angle of attack of an airfoil is too large then big eddys form at the leading edge. this is called 'stall', the plane loses altitude. Ask yourself what too large an angle of attack would lead to with a prop.

Prop cup is just like dropping the flap on the trailing edge of an airplane wing, it increases the circulation about the foil by shedding more vorticity off the trailing edge (the latter is drag, and to keep lift/drag high the foil's wake, the vorticity shed in the form of helices from a prop blade) must remain thin. I played with leading edge camber in 1978 before any outboard prop specialist thought about it. Actually, some Fla. racers looked at my props and tried to copy, then in 1981 or so we got props from OMC and Mercury with some leading edge camber. I'm not about to say 'why' that's important, I never got enough together either empirically to write an article about it.

I have read that advanced research always presents angle of attack as the strongest force in lift.

Going thinner and increasing angle of attack increases lift, which is contrary to "airfoil" lift theory. A wing has lift if it has angle of attack, regardless of how thin it is.

[Mark75H]

Yes, "stall" comes in at the extreme of excessive angle and low speed, I was referring to the other end of the curve.


All wings and props meet a stall limit somewhere, even yours.