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Prop solidity and efficiency

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Prop solidity and efficiency

Old 20th Jul 2008, 21:59
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Prop solidity and efficiency

not sure if this is the right section but seems the most appropriate place.

studying for my JAA ATPL grounschool and have this question.

with regards to efficiency where prop efficiency = (thrust x TAS)/(RPM x Torque)

it asked what happens to efficiency when solidity were to increase. now i thought that increasing solidity would increase the power that could be absorbed by the prop thus the thrust should increase resulting in increasing efficiency. however, the answer was the opposite, i.e. increasing solidity would decrease efficiency.

could anyone explain?
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Old 20th Jul 2008, 22:30
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studying for my JAA ATPL grounschool
could anyone explain?
Your instructor, perhaps...?
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Old 21st Jul 2008, 00:56
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I'm usually pretty good on this stuff - but this is the first time in 20 years that I have heard the term "prop solidity" !!

Sure you know what you are asking?
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Old 21st Jul 2008, 01:26
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'Solidity' is indeed a valid prop parameter, think its the frontal area of the blades / swept area of the baldes (i.e. disc area).

More blades or wider chord, higher solidity
Contra-rotating prop, doubles it I imagine

I'm stabbing a bit here, being much more than 20 years ago..

But solidity would be increased to absorb more power from the same diameter (disc area), e.g. Spitfire prototype started off with a 2-bladed fixed pitch prop just under 10' diameter, ended up with either 5-bladed Rotol prop of 10'6" or in the Seafire's case, a contra-rotating prop with 2 sets of 3 blades.
This because power went from about 900 HP on the prototype to something like 2,200 Hp (maybe more) in the later Griffon engined versions Seafire) and yet prop diameter was severely constrained by layout and undercarrige length - hence increasing solidity.

Efficiency I think comes down to the difference between inflow and outflow velocity, very much like a turbojet VS turbofan, where the lower outflow velocity of a fan (but over a greater area) increases the efficiency.
A higher solidity prop would increase the ratio Vout/Vin, decreasing efficiency, one really wanting a smaller change in velocity added but over a larger area.

Propulsive efficiency isn't about how much air you can throw behind you and how much energy you can add to it, it's about how little energy you use to add a 'given amount' of energy to the propulsive medium (air)

However, I'm sure tip-speed comes into this as well, as anywhere near transonic conditions will ramp up the prop blade drag and reduce efficiency...

Having just opened Aerodyanmics for Engineering Students, Houghton & Brock..

Ideal Froud efficiency of an airscrew = 2V/(Vs+V) where V is the freestream velocity and Vs is the final velocity in the screw's wake, so as that increases efficiency reduces, Vs being in the denominator.

Another form of that formula is V/Vo (where Vo is the velocity in the plane of the disc, less than Vs but of course greater than V, the free-stream velocity)

Any real airscrew will have an efficiency less than the ideal Froude of course, but that is the basis of propulsive effciency, and a higher solidity will increase VS and reduce efficiency.

Nice to know it sort of fits my gut instinct expressed above

And hope that helps a bit

Last edited by HarryMann; 21st Jul 2008 at 01:38.
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Old 21st Jul 2008, 03:58
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More solidity, less efficiency, is correct.
Generally speaking, the more blades, the less efficient the propellor...for cruise.
Of course, a whole lot depends on the blade cross section, width, length, rotational speed, etc.

Take a Cessna 182 as an example.
Two varieties of propellor are offered, two and three blade.
Three blades would be desired if maximum takeoff/initial climb performance was of importance.
The two bladed propellor would however, generally produce the highest cruise speed (a knot or two) provided the same engine conditions were met...BHP and rotational speed.
To maximise the speed increase, the lowest usable RPM would be desired.

Reason?
Less drag due to the fewer number of blades.
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Old 21st Jul 2008, 09:19
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Having just opened Aerodyanmics for Engineering Students, Houghton & Brock..
Showing your age Harry! Houghton and Brock became Houghton and Caruthers in the early 1980s, became Houghton and Carpented in the mid 1990s. Carpenter died this year and presumably the publisher is looking for yet another co-author.

Whether the legendary Ted Houghton is still alive on a machine somewhere, or died years ago and they're just re-using his name, I've no idea.

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Old 21st Jul 2008, 10:06
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The efficiency effect is more easily seen if you use the actuator disc analogy.
More solidity means you are accelerating the flow in the stream tube to a higher outflow velocity to get the extra thrust.

The work input is proportional to v^2*mass flow whereas the thrust output is proportional to v*mass flow.

To retain the same propulsive efficiency requires a bigger actuator disc and keep the same outflow velocity, but with a bigger mass of air.

This is the same reason that high bypass ratio turbo-fans are more efficient than low ratio ones
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Old 21st Jul 2008, 10:34
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A good example of this "solidity" is the Hercules. early models with Allisons had 4-blade props with high solidity ratio. The newer c130k have 6-blade props with low solidity. Judging by the relative prop noise from a Fat Albert with 4-blades they must be less efficient.
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Old 22nd Jul 2008, 09:17
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The simple student explanation: The blades of a propeller interact with each other, in a manner which decreases efficiency. If you think of the blades as wings, each blade will be operating in the downwash and disturbed wake from the preceding blades. More blades mean more interaction means less efficient.

An analogy is double/tripledecker designs vs. monoplanes.

Model aircraft pylon racers have an interesting approach to this. They use one-bladed propellers, balanced with a counterweight.
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Old 16th Jan 2022, 00:15
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Efficiency

Originally Posted by pilotho View Post
not sure if this is the right section but seems the most appropriate place.

studying for my JAA ATPL grounschool and have this question.

with regards to efficiency where prop efficiency = (thrust x TAS)/(RPM x Torque)

it asked what happens to efficiency when solidity were to increase. now i thought that increasing solidity would increase the power that could be absorbed by the prop thus the thrust should increase resulting in increasing efficiency. however, the answer was the opposite, i.e. increasing solidity would decrease efficiency.

could anyone explain?
You are correct that the higher the solidity ratio, the higher the work absorption or the amount of fluid that will be moved, which in your context is thrust. However, the relationship is very non-linear. That is doubling the solidity ratio does not double the work absorption and in fact as solidity ratio would approach unity, diminishing returns dominates and work absorption essentially tops out well before reaching that point. So the question to be answered is why the relationship is non-linear. Probably one of the biggest contributors would be drag on the blades. Increase the number of blades from two to three and the drag would increase by 50%. Hence the drag is an irrecoverable parasitic loss that increases faster than the work absorption. Therefore, as solidity ratio increases, the efficiency decreases.
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Old 16th Jan 2022, 03:02
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Hopefully this will enable you to find the answer after doing a bit of arithmetic http://wpage.unina.it/fabrnico/DIDAT...-Propeller.pdf

an extract from Dr John Lowry’s book mentioned here (they removed the charts so see the book) https://www.avweb.com/features_old/t...ler-airplanes/

correct term is total activity factor (blade activity factor multiplied by the number of blades) rather than solidity

(I wonder what their source document for their question was)

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Old 16th Jan 2022, 06:40
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Hopefully after fourteen years the OP passed the exam. Then again, he or she possibly forgot all about it….
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