How to calculate propeller pitch speed, airplane max speed and motor RPM

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This article will explain how to calculate the estimated max speed your RC aeroplane can reach for a given propeller and motor KV.
We are going to go through:

To start our take on this subject we first need to explain:

  • What is Motor KV?
  • Explain the term Propeller pitch.
  • How to calculate propeller pitch speed?
  • How to estimate max flight speed?

Where shall we start then?

Motor KV is a constant, a rating that every motor designed for this hobby has in its specification. It defines how many times motor will rotate per every Volt if there is no load applied.
Still not clear? Let's go with an example. Motor rated to 1KV will rotate 1 time per sec per volt. This means if you apply 10V to this motor, you can, theoretically, spin it with 10RPM if there is no load (Propeller etc.) put on it.

Modern RC brushless motors are rated between 700kv for large and heave aeroplanes to around 2800kv for 5" racing drones running 4S Lipo Batteries and higher if required.
Typical 5" racing drone, built for 4S lipo uses 2450kv motors.
Having the motor KV rating we can calculate the max rotational speed of this motor without a propeller for a given battery voltage.

Let's do that then...

4 Cell LiPo (4S) when fully charged, has the voltage equal to 4 x 4.2v = 16.8v

Having the voltage we can next use our formula (Motor KV  x  Voltage = RPM) to calculate the max rev of this motor... Let's do it then. 

2450 x 16.8 = 41160RPM !

Easy enough? good!

 

We need one more thing before we start estimating the max speed your aeroplane can reach, what brings us to the next mysterious term, Propeller pitch.

To understand Propeller pitch parameter You need to imagine a propeller as it is screwing into the air same way screw goes into a nut.

Propeller pitch is usually expressed in inches. Value of the propeller pitch describes how far the prop will screw into the air per revolution. Oh yeah! 100% efficient propeller with the pitch of 4" will move foreword 4" per revolution into the air. At this point, you are probably starting to see where this is going. We know how fast the motor can spin in revolutions/sec and how far the propeller can push in this same time. That's right! It is that simple.

 

The propeller pitch speed is the speed with witch 100% efficient propeller will move through the air for the given speed of the motor rotation. 

So what's next? Well, it is time to talk about calculating Flight max speed.

Aeroplane max speed can be anywhere between ~60% to ~80% of the propeller pitch speed depending on a whole bunch of variables including prop efficiency, the density of the air that can be affected by the temperature, aeroplane drag and the relative speed of the aircraft against the air... 

The raw formula for the max aeroplane speed is:

pitch speed formula

Pitch speed in mp/h = RPM x Prop Pitch x (60/63360) 

Pitch speed in km/h = RPM x Prop Pitch x (60/63360) 

So the next thing you need is to add the efficiency variables... Not going to lie to you, this is a hard one.

Motor efficiency under the load, and it's maxed RPM depends on a lot of things like: propeller efficiency at the given speed, let's call it a P-factor. The motor itself can be generally more or less efficient. Let's call this one an M-factor... next thing is the battery! Voltage drops under the load so you are not able to get full power out of the rated motor KV, this is the B-Factor. The motor max RPM drops when you include those M, P and B-factors, unfortunately, common people are not able to take those into an account with high precision. Well... we are not common people so we are going to anyway :) 

Let's try some examples:

Aeroplane flyes with a 4" pitch propeller. Its motor is 2450KV and the battery voltage = 16.8v (4s Lipo)

M-Factor we are estimating to about 80% / 0.8 (base on my experience. This is about the 20% drop in the system efficiency caused by the motors imperfection)

P-Factor = 90% / 0.9 (The 10% drop in the system efficiency caused by the drag on the propeller)

B-Factor = 90% / 0.9 (10% drop in the efficiency caused by the battery voltage drop under load ) 

Our motor does 41160RPM x (B+P+M-Factor) of 0.6 = 24696 RPM UNDER LOAD

So if we plug that into our calculations we get:

24696rpm x 4" x (60/63360) = 93.5mph.

Wasn't that hard? Good!

In the reality, the speed you might be able to get out of it will quite likely be lower than this due to the force of drag generated by the aeroplane itself. We are not going to include it as it opened an entire can of worms on its own. You can add another factor if you feel like it but the estimating technique above should give you pretty good results without it. Just remember, faster you go more air drag you fight against.

That's it, I hope this helps you understand your model dynamics a little more.

All the best and thank you for reading.

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