How does the Kv work in this rule of thumb? Such as Kv per ounce or Kv per pound?

1) commit aviation (very sedate slow flyer) you need at least 50W/lb
2) for a trainer 75W/lb
3) for sport plane 100W/lb
4) for pattern about 125W/lb
5) for full on 3D anything from 150W/lb upwards

From : Don Stackhouse

As is often the case, another simple question, with an answer that is anything but.

First of all, that list is another one of those "rules of thumb", with all the limitations inherent in them. In this case the numbers apply to only a certain range of models, probably about the Speed 400 and up sizes of outdoor models, with conventional propellers, and conventional wing loadings and span loadings. If you get into things like sailplanes with high efficiency, low drag and low flying speeds, you can get good performance with less power. However, something with relatively poor propulsive efficiency such as a ducted fan, you'd better have more power. Likewise, something with a high wing loading (and therefore a higher than "normal" flying speed) has a greater amount of parasite drag to deal with, so it will need more power. OTOH, something that's designed to fly slower will need less.

For example, the models typically cited for this rule probably operate in the range of the high teens to the low thirties for airspeeds, and the 50 watts per pound number is appropriate in that context. However, a small "park flier" such as our 3 ounce Curtiss-Wright "Junior" can get comparable performance (within the context of its 10-15 mph typical cruising speed) on only about 30 watts per pound, because the lower flying speed results in considerably less parasite drag, and the low span loading helps the induced drag.

Kv really addresses a different issue, the relationship between the motor and the prop. Here it might help to draw an analogy with the common automobile. If the motor of the model corresponds to the motor of the car, then the prop (and anything between the prop and the motor, such as a reduction drive) corresponds to the car's transmission, drivetrain and wheels.

The motor of the car generates mechanical energy, and the transmission, drivetrain and wheels transfer that mechanical energy from the motor to the road (which, through Newton's third law, the one about action and reaction, applies an equal and opposite reaction to the car).

In an airplane, the motor generates mechanical energy, and the prop (plus any reduction drive) transfers that mechanical energy from the motor to the air, which (in accordance with Newton's third law) applies an equal and opposite reaction to the airplane.

Now, the key item in both of those relationships is the ratios involved. In the case of the car, we have a motor that is happiest when running at some RPM when at some given power setting, and the car wants to move along the road at some speed when at that same power setting. The drivetrain designer has to come up with gear ratios and tire diameters for that set of operating RPMs and operating speeds, that matches the desired RPM of the motor to the desired speed of the car. Of course in the process the designer also has to consider how big a patch of rubber is required between the tires and the road to efficiently transfer the power without skidding, and the tradeoffs between the rolling friction, the traction required, the handling qualities, and a variety of other factors that constrain the tire diameter and width. This then forces the decision on the ratios of the gears in the rest of the drivetrain.

In an airplane we have constraints on the diameter and pitch required in the prop to efficiently transfer power to the air, and the desired RPM that results from that situation. In general this tends to be a relatively low RPM. On the other hand we have the RPM desired by the motor, which in general tends to be a fairly high RPM.

If we can come up with a way to reconcile these two conflicting requirements, we can get away with a direct-drive system. Examples of this are relatively low-powered airplanes with high Kv motors, where the power is low enough that we can get away with a small prop that tolerates running at a high RPM. Another example is the typical "outrunner" motor such as the one I have in my electric 2-meter Chrysalis. The outrunners as a group tend to have low Kv's, so they are happy when running at a relatively low RPM's, which then allows for a large prop diameter and fairly high powers with direct drive.

However, if we can't reconcile the needs of the motor for high RPM, with the aerodynamic need for a large diameter prop (which therefore limits the prop to relatively low RPM), then the solution may be to insert a reduction drive between the prop and the motor to let each of them run at their desired speed.

OK, that sounds great, but what about the case where we have to run at a variety of power settings and speeds? For example, the typical reciprocating car engine is only efficient over a relatively narrow range of RPM's. If we have a wide range of speeds we want to drive at, wider than the engine's range of useful RPM's, then we have to resort to a transmission in the drivetrain that has more than one gear. If we want to relieve the driver of the work of figuring out which gear to use for best motor efficiency, we can even go to an automatic transmission.

The analogous situation in an airplane is the variable pitch propeller. Changing the prop's pitch is like changing the gear ratio of the car's transmission. If we really want to hold the motor precisely at its most efficient RPM, and without relying on the pilot to readjust for every little change in the airplane's speed, altitude and flight path, then we automate the process by adding a governor, and making the prop a variable pitch, constant speed prop. That's right, a variable pitch, constant speed prop is the airplane equivalent of a car's automatic transmission.

Note, we only need that extra complexity if we have a wider range of operating conditions than the motor can tolerate. In planes or cars with only a narrow range of operating speeds, or with motors that tolerate wide ranges of motor RPM's, we do not need the extra complexity, weight, cost, and efficiency penalties of a variable speed transmission system. Most of our model airplanes fall in this category, as do things like some types of golf carts. Also, a free-turbine turboshaft engine typically has an extremely wide range of efficient RPM's, so some of those turbine powered cars and trucks that various companies were experimenting with back in the 60's and 70's only needed a one-speed transmission.

But I digress... Getting back to the original question, how does Kv relate to the size or weight of the model? The short answer is, it doesn't. As is typically the case where the relationship involves more than two variables (a lot more than two in this case), any attempt at making a "rule of thumb" quickly drowns itself in a veritable ocean of exceptions. However, we can draw some general inferences:

Lower Kv (i.e.: a motor that naturally likes to run at low RPM and high torque) increases the chances that we can successfully operate "direct drive" needing no a gearbox between the prop and the motor.

Eliminating the reduction drive gets rid of the reduction drive's efficiency losses, which could typically be anywhere from a 3% penalty to 15% or more, depending on the design details and the operating parameters. However, generally a low Kv motor (such as a typical outrunner) pays a penalty in the motor's electrical efficiency (I've heard that it's because of increased "iron losses" in the motor, but I'll leave it to the electric motor experts in this group to cover that issue). Which approach results in the smallest efficiency losses depends on the individual case.

In addition, reducing the prop RPM typically allows for an increase in prop diameter, which typically results in more prop efficiency. However, this is not automatically true, there can indeed be such a thing as too much prop diameter, just as there is such a thing as too many blades, or too few blades. Once again, each individual case has to be evaluated on its own merits.

One other thing that enters into this issue of prop efficiency is the range of operating conditions. It's usually possible to design a prop with pretty decent efficiency at one particular operating airspeed, altitude, RPM and power setting. However, very few airplanes fly at only one flight condition. Determining a basic Kv, gear ratio and set of prop parameters becomes a far trickier problem if you have to operate efficiently at a range of flight conditions. The prop that has extremely good efficiency at one flight condition might be extremely "peaky", so that its performance drops off very suddenly with even a small deviation from that design flight condition. This is especially important for fixed pitch props.

There are references that can help find a better baseline design point. Unfortunately these tend to be scarce as hen's teeth, and even if you have one, you still need to know how to use it. The design of a prop, and the matching of a prop to an airframe and engine, is one of the most complex and difficult jobs in airplane design, but also one of the most misunderstood and underestimated.

So, we come down to the one rule of thumb that does seem to hold up consistently in engineering:

The design with the greatest probability of success is the one where the designer did their homework thoroughly, and addressed all the interactions of all the relevant details of that particular design, instead of relying too much on oversimplified rules of thumb!

Don Stackhouse
DJ Aerotech