4 bladed props

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a three blade prop has a higher efficency but the diameter of the prop to accept the greater HP would exceed the length of the landing gear so the only way around was to add more prop blades. However, there are some sources that claim that a four blade is more efficent at high altitude.

Hope that helped

Umnh, no. Since I did prop aero for a number of years, I know that the statement "three blade prop has a higher efficency[sic]" is, at best, an oversimplification. Induced losses are reduced with a greater number of blades; the loss of efficiency with greater blade numbers will occur if individual blade chords are excessively large or if there is interference between blade roots; the latter does not tend to be problematic with as few as six blades, and not until speeds that are greater than the operational speeds of almost all ww2 aircraft (modern propellers, such as those on the A400M, have the spinners contoured to eliminate that problem This requires cfd tools that didn't exist 30 years ago and weren't possible 50 years ago). There is a constraint on minimum blade chord; this is usually that the blade operates with large regions of separated flow and with highly angular airflow in the propeller in some flight regimes, especially takeoff, and this dictates the thickness at the blade root, which will tend to dictate the minimum chord.
 
There is another point of diminishing returns and that is frwer blades. They found out in the 1930's about aeroelasticity of the prop adn discovered that high-powered 2-bladed props were prone to shed blades after too much flexing during takeoff and high-power runs.

You may remember that Jum Wright made a replica of the Howrd Higes racer, complete with the same engine and prop. He was warned by several people that the 2-blade with the Hornet engine was a dangerous combination but, while flying back to Oregon from Oshkosh, he shed a prop blade and crashed.

That may or may not have anything to do with flexing. There are many reasons for a prop to shed a blade.
MacCauley have been trying for 20 years to get one of their propellers to work with the one of the Lyc IO-360 series engines (I can't remember which one off the top of my head) and just can't get it to work. After 20 hours of operation, the blade shears off at the root. There is something happening that the engineers just can't quite nail down, and these aren't high-powered engines.
 
Some of the early WWI English biplanes had four-bladed propellers. The BE 2-C, described charitably as 'perhaps the worst plane ever made" (up to that point). British ace Albert Ball summed it up as "a bloody awful aeroplane".

As early as 1915, the B.E.2c entered service as a pioneer night fighter, being used in attempts to intercept and destroy the German Zeppelin airship raiders. The interceptor version of the B.E.2c was flown as a single-seater with an auxiliary fuel tank on the centre of gravity, in the position of the observer's seat. After an initial lack of success while using darts and small incendiary bombs to attack airships from above, a Lewis gun was mounted to fire incendiary ammunition upwards, at an angle of 45°, to attack the airship from below. The performance of the B.E.2 was inadequate to intercept the Gotha bombers of 1917, but the techniques it pioneered were used by the later night fighters.


View: https://www.youtube.com/watch?v=yvA-154kgrM
 
sqrt = square root.

The ideal diameter of a 2-blade prop in inches would be 22 * sqrt(HP).

The diameter of a 3-bladed prop would be 18 * sqrt(HP).

The diameter of a 3-bladed agricultural prop would be 20 * sqrt(HP).

The 4/5-blade I don't have yet, but these ar VERY close ... and the REAL diameter depends on use and landing gear length. A Naval fighter would need a shorter prop than an Air Force fighter due to carrier landing thumps.

Good place to start your prop investigation ...
 
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Caproni Ca 161 bis - the airplane with which Col. Mario Pezzi achieved the world record height for propeller driven aircraft, still unbeaten with 17.083m, october 1938.
 

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a three blade prop has a higher efficency but the diameter of the prop to accept the greater HP would exceed the length of the landing gear so the only way around was to add more prop blades. However, there are some sources that claim that a four blade is more efficent at high altitude.

Hope that helped

It doesn't, because it's wrong. Propellers, like any other lifting device have two loss mechanisms: profile drag, which comprises skin friction drag and (possibly) compressibility drag, if there are any normal shocks on the surface, and induced drag. The former is a strong function of blade area and geometry; the latter is proportional to the lift squared on each blade. Blade area is dictated by blade loading, measured by thrust coefficient. If you need X square feet of blade in a given diameter, you want to spread it among as many blades as practical: double the number of blades, the lift per blade is halved, and the induced drag per blade is reduced by 75%, so the net induced drag is reduced. On the other hand, the minimum chord (and thickness:chord ratio) is dictated by structural demands, especially at takeoff, where the blade is largely stalled.

The other advantage of more blades is that the force required per blade from the pitch change mechanism is roughly proportional to the blade chord times blade area, so pitch change mechanism for a propeller with more blades doesn't need to provide as much force.

The propeller with the lowest induced drag is one where you spread the required blade area over an infinite number of blades, but this is a trifle difficult.

So, in favor of more blades: lower induced drag, lower loads in the pitch change mechanism and lower blade weight. In favor of fewer blades: lower cost of manufacture, more blade damage tolerance, fewer structural problems during takeoff conditions.
 

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