2 vs. 4 bladed props, which is more efficient, faster, climbs better, etc.?

Well, I see there's a lot of controversy going around now about 2 vs. 4 bladed props, which is more efficient, faster, climbs better, etc.. The answer is that there is no one single right answer. It depends on the aircraft, motor and prop combination, and on the flight condition.

There are basically two kinds of aerodynamic losses at work in a propeller, "profile" and "induced". Profile is the energy losses resulting from moving the blades through the air (the propeller equivalent of parasite drag), while induced losses are those that result from the production of thrust (the propeller equivalent of induced drag for a wing).

Let's assume we've already determined a diameter. For a given set of operating conditions (diameter, horsepower, airspeed, altitude, rpm, etc.) there is an optimum number of blades. In all probability, even on the same aircraft there will be a different optimum for each flight condition, so whatever we decide will be a compromise at best.

One of the most basic forms of propeller analysis is what's called "actuator disk" theory. In this approach, a propeller is a theoretical disk that causes any air that goes through it to accelerate. This theory ignores things like uneven inflow, and more importantly it assumes that the power is spread evenly over the entire disk, like the peanut butter on the world's most perfectly made PBJ sandwich.

In the real world things aren't quite so perfect. The power from the motor is spread over the disk by the propeller blades, but for a finite number of blades they can't get it spread perfectly even across the entire surface. With only two blades the power gets concentrated in two radial stripes, with a relatively thin layer of peanut bu... oops, I mean power, spread over the rest of the disk. Whenever you concentrate a lot of power into a relatively concentrated space, the induced losses get worse. By adding blades we can spread the power more evenly over the disk, and improve on those induced losses.

So let's all use 10,000 bladed props, right? Well, not quite. Two things get in the way. If you increase the number of blades, those blades need to be narrower. For a given amount of power you need roughly the same total blade area to absorb it in a given diameter, so that area divided among more blades means the blades get skinnier.

One side effect is that with their chord now reduced, their Reynolds numbers get lower, and you all probably know what happens to the efficiency of airfoils when their Reynolds numbers (a.k.a. "Scale effect"; chord times speed times air density divided by air viscosity) get smaller.

An even bigger effect in most cases (at least for full-scale props) is that their profile losses get worse. We're moving a greater number of objects through the air, so we create a bigger stir and lose a greater amount of energy doing so. More blades means lower induced losses, but higher profile losses.

High power/low speed situations like takeoff and climb are dominated by induced losses, so more blades tend to help there. Cruise and other high speed flight conditions have higher mass flow through the prop (because of the higher speed), so they tend to be more sensitive to profile losses. Just as with an aircraft, where the highest L/D will occur when induced drag is exactly equal to parasite drag, for a propeller the optimum number of blades in any given flight condition will be where the induced losses are equal to the profile losses.

Noise is a bit more complicated, but follows similar principles. The total noise is composed of two contributors, "pressure" noise (due to the pressure differential across the blade that results from making thrust, it's the noise equivalent of induced losses); and "thickness" noise, which is analogous to profile losses, it's the noise created just by the disturbance of the blade passing through the air. If you add blades you're moving more objects through the air, making the thickness noise worse, but you're dividing the power up into smaller pieces and making the pressure noise better. Once again, the total sound pressure will be lowest when the thickness noise and the pressure noise are equal (funny how that same principle keeps coming up, isn't it?).

Unfortunately that's not the end of it. We have several different criteria for measuring sound. One of those measures the absolute sound pressure, irrespective of frequency content. We call that the "DbL" scale. There's another scale where the sound content at different frequencies is weighted to represent the sensitivity of the human ear. We call this the "DbA" scale, and instead of measuring the absolute loudness of a sound, it's more a measure of how annoying it is. In general the DbA scale gets more sensitive at higher frequencies. Because of this, adding blades (which increases the frequency of the propeller noise) can often lower the DbL noise (by dividing the power up into a larger number of smaller pulses), but raise the DbA noise (by moving the the frequency up into a more sensitive area of the DbA scale). There's still one more quirk left; even though the higher frequency sounds might look bad on the DbA scale, they often don't "carry" as well, damping out more quickly in a shorter distance.

The biggest single factor in propeller noise is helical tip speed, the combination of the rotational velocity of the blade tip and the forward speed of the aircraft. Propeller efficiency goes downhill very quickly as the tip speed gets near the speed of sound (contrary to popular belief, propellers almost never are designed with tip speeds near Mach 1.0). As a general rule of thumb, for efficiency purposes the tip Mach number plus the thickness to chord ratio should never be more than about 0.9; for example, if the tip airfoil is 2% thick, the tip Mach number should be less than 0.88 . Well before this limit, the noise will probably become unacceptable. I remember hearing of some tests NASA did back in the 50's and 60's with props mounted to turboprop engines on the noses of supersonic jet fighters, just to see what would happen to prop performance at transonic speeds. What happened was a lot of angry neighbors and some test pilots with permanent hearing damage.

Even small decreases in diameter can reduce tip speed sufficiently to significantly reduce noise. That's often the rationale for retro-fitting props with a greater number of blades onto full scale aircraft; the more even distribution of power over the disk allows for a slightly smaller diameter without losing efficiency, which in turn reduces tip speed. On twin engine aircraft a diameter reduction can also increase the clearance between the blade tips and the side of the fuselage, which can dramatically improve cabin noise.

So what should you use on your model? Unfortunately there's no simple answer to that one. Like I said in my last post, props are like shoes; they have to be fitted individually to each specific application, and the size and design that fits one situation will probably not work for something even slightly different. There are some fairly complex methods to get things in the ballpark, but even those don't apply to models without some judgement. In the end, unless you have access to some fairly sophisticated computer codes for simultaneously optimizing diameter and the distributions of camber, thickness, chord and especially twist, your best bet probably is to do a lot of flight testing. And yes, when your spouse complains about all the flying you're doing, you have my permission to tell them that I recommended that you do this! :-)

Don Stackhouse @ DJ Aerotech