The Propeller as a Rotating Wing

Prove the analogy before relying on it.

1. Cut a short section of aerofoil identical to your best wind-tunnel result.
2. Mount it in the tunnel and record lift and drag at a few angles, as before.
3. Now reason about what that same section experiences when it is instead sweeping a circle at radius r and turning at n revolutions per second.
4. Work out the speed it meets the air: the vector sum of the aircraft’s forward speed and the rotational speed 2πrn.

The section does not know or care whether it is flying straight or going round in a circle — it only experiences a relative wind and an angle to it. That is the whole insight. Lift becomes thrust because the section is oriented so its lift points forward; drag becomes the torque the engine must overcome.

Do the arithmetic that produces the shape, so the shape stops being mysterious.

1. Choose a design forward speed V and a rotational speed n.
2. Divide the blade into stations at, say, 25, 50, 75 and 100 percent of the radius.
3. At each station compute the rotational speed 2πrn and the resulting helix angle, whose tangent is V divided by that rotational speed.
4. Add your aerofoil’s best angle of attack to the helix angle at each station. That sum is the blade angle there.
5. Tabulate the four blade angles.

The angles fall steeply from root to tip — often from around 40° near the hub to under 15° at the tip. The blade is not bent for strength or elegance; each station is individually aimed so it meets the air at the angle the tunnel said was best.

Cut the numbers into wood, one station at a time.

1. Start from a rectangular hardwood blank of the right length and thickness, with the centreline marked on all four faces.
2. Mark the four stations across the blank.
3. At each station, cut a gauge from card at the calculated blade angle.
4. Carve down to each gauge in turn, working from tip to root, then fair the surface smoothly between stations.
5. Shape the aerofoil section on each blade face, thicker at the root and thinner toward the tip.

Fairing between the stations is where a propeller is made or ruined. The four gauges only fix four sections; the surface between them must run smoothly, because any local bump or hollow produces flow separation and both loses thrust and makes noise.

An unbalanced propeller is a vibration source bolted to the front of the machine.

1. Mount the finished propeller on a free-running horizontal spindle with very low friction.
2. Let it settle. If one blade consistently swings to the bottom, that blade is heavy.
3. Remove material from the heavy blade’s FACE — never from its edges or tip profile — or add weight at the light blade’s root.
4. Repeat until it shows no preferred resting position.
5. Also check horizontal balance: the blades must weigh the same at the same radius, not merely weigh the same.

An out-of-balance propeller applies a rotating force at the shaft frequency, which fatigues the mounting, blurs instruments and cracks structure over time. The mass involved may be a gram; the force scales with the square of the rotational speed, so a gram at 3000 rpm is not a small thing.

Now find out whether the calculation was worth doing.

1. Mount the propeller on a motor fixed to a pivoted arm, with a spring scale reading the thrust it produces.
2. Measure thrust and rotational speed together across a range of speeds, along with the electrical power going in.
3. Compute thrust per watt at each speed.
4. Now compute the TIP speed at each: 2πRn.

Thrust per watt improves with speed and then falls away, and the fall begins as tip speed climbs toward the speed of sound. As the tip approaches roughly 0.85 to 0.9 of sonic speed, local flow over the blade goes supersonic, shock waves form, drag rises steeply and efficiency collapses — and the propeller gets very loud, because that noise is the energy you are no longer converting to thrust.

This is the hard ceiling on propeller-driven flight, and it is the reason the batch ends where it does. You cannot spin faster and you cannot usefully make the blade longer, because a longer blade has a faster tip at the same rpm. The propeller runs out of road at somewhere around 700 km/h, and the only way past is to stop using one.