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I currently am creating a project in which I'm using a 1045 propeller with a BLDC motor that spins at ~16,000RPM. It is powering a single motor "rocket" that basically is configured to carry a payload to ~380m. I've done a lot of testing with the rocket and found that it's reaching all the altitudes and speeds correctly. However, the rocket spins quite a lot in the roll axis. The payload that I'm carrying is actually meant to benefit from the centrifuge that the rocket is acting like but I would like to calculate the exact centrifugal force created by the propeller.

$$F = \frac{m v^2}{r}$$

I used this formula for calculating the centrifugal force created by the propeller. Since I know the angular velocity (16,000RPM) of the propeller, I calculated the tangential velocity to be 207.76m/s.

Mass of propeller - 28g

Velocity = 217.8m/s

Radius = (25.4/2) = 12.4

I got, F = (0.028) x (207.76)² / 0.124

Which gave me, F = ~9747N. That's 35,498g of acceleration.

I personally think something is wrong with that, isn't it excessive? Or am I just mistaken?

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    $\begingroup$ When the propeller spins, it makes the rocket spin the other way around as per Newton's third law. To calculate the two mutual rotating speeds you need to apply Newton's second law and that's why I think this question is better served on physics Stackexchange $\endgroup$
    – sophit
    Jan 22, 2023 at 8:44

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Problems I found:

  • You are calculating the centrifugal force of the propeller, not the payload (unless the payload is spinning with the propeller - or perhaps if payload is the propeller itself).

  • Radius is incorrect. When calculating centrifugal force, "radius" is not simply the shaft-centre to blade-tip distance - it is the distance between shaft-centre and the CG of the prop blade.

  • Mass is incorrect. It should be 14g - the mass of one blade, not the entire prop. (And regardless, it is supposed to be payload mass, not prop mass).


Suggestions:

In the question, it appears that the rocket is spinning due to the propeller torque (like a helicopter without tail rotor). You first need to determine the rotation speed of the vehicle - excluding the prop.

Next, you need to determine the CG of the payload, and that of the rocket with the payload installed. The distance between the two CG's is the radius. From here, you can determine the tangential velocity of the payload. Finally, measure the payload mass and from there you can calculate the centrifugal force.

However, this is only helpful if you assume a point-sized payload. For accuracy, I would instead recommend that you directly calculate the acceleration at the part of the payload you're concerned with (unless the payload size is small compared to the radius).


Determining vehicle rotation speed

For obvious reasons, this is no easy task; so here are some solutions.

  1. Determine Experimentally: Attach the vehicle to a pivot on its rolling axis, and select the normal flight power. To prevent vehicle breakdown, consider encasing the vehicle all around with a structure that may arrest it. The steady state vehicle RPM in this case will almost certainly be higher than what it would be in flight. If available, you can use a powerful fan blowing onto the vehicle from above - to simulate the real flight.

  2. Make a simple RPM sensor: Install an LDR (Light Dependent Resistor) to a side of your rocket, figure out a way to accurately time its output pulses, and launch the rocket in morning/evening on a sunny day. If all goes well, the number of pulses in a given time should give you the RPM.

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  • $\begingroup$ The rocket is spinning due to the propeller being at the top. I wanted to calculate the centrifugal force that the payload is being subjected to. And yes, the rocket spins just like a helicopter with a missing tail rotor. Determining the rotation speed would be quite complicated for me, so I thought that I could calculate the rotation speed. $\endgroup$ Jan 22, 2023 at 8:31
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    $\begingroup$ @AadirajAnil I understand how complicated it would be to determine the rotation speed, but I can assure you that prop RPM would be quite different from the vehicle RPM. Also, I didn't get why you used prop radius and prop mass in your calculation, where you should have instead used payload radial distance as "r" and payload mass as "m". (Also, I have an idea to calculate the vehicle rotation speed - it's kind of a jugaad but it might give a good approximation, let me know if I can help.) $\endgroup$ Jan 22, 2023 at 8:45
  • $\begingroup$ I used prop radius since I'm new in the area and was confused. It would be great if you could help with the vehicle RPM, even if it's a jugaad! $\endgroup$ Jan 22, 2023 at 8:58
  • $\begingroup$ @AadirajAnil Alright, give me some time, I will add that to my answer :-) $\endgroup$ Jan 22, 2023 at 8:59
  • $\begingroup$ @AdityaSharma and Aadiraj: to get the rotating speed of the rocket's body, CG is not enough, you need the moments of inertia of the propeller and the rocket's body. Afterward you can apply Newton's second law to estimate the two rotating speeds. Or you just do some testing but I don't know if it's easier (for sure more funny). $\endgroup$
    – sophit
    Jan 22, 2023 at 9:50
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A similar issue was observed with a solid fuel model rocket. The good news is that spin can be stopped and even controlled to a specific rate with fins.

The spinning forces here are not unlike those found in single prop aircraft and helicopters. What makes it particularly interesting is that, with the high RPM of the prop, and less rotational drag resistance, the rocket spin rate may become quite high.

First, control it, quantify it, then adjust it by fine-tuning how much spin resistance you want.

A limiting factor here is, as spin rate increases, prop thrust decreases because relative to the free stream of incoming air, prop rpm slows down. Even though 16,000 rpm is quite high, you may have noticed a decrease in the rockets forward speed as it spins up.

With fins, rotational motion of the airframe or body they are attached to changes their relative wind, giving them anti-spin lifting force qualities.

The spin will reach steady state rotational velocity when prop/engine torque is balanced by fin/body resistance torque along their respective radii.

This is bound to happen quickly as torque is great, and mass and radius are low. Rotational V zero to Rotational steady state may be on the order of a few seconds.

As in the early days of full scale rocketry, alternating stripes can be added on so photography (back then frames per second) could be used to determine spin rate.

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