Measuring the speed of a Frisbee & Boomerang

[LazyBoy]

Hello everyone,

I am new to this forum but been thinking up gadgets and creating fun little projects for just over 15 years now...

I was wondering if a tiny button cell battery powered pcb with a Bluetooth accelerometer fitted into the centre section of a Frisbee or Boomerang would be able to record and transmit data to a paired smartphone for the display output?

Any thoughts?

 

[Anon_LG]

Hello, welcome.

Problems with using the accelerometer:
1. It measures acceleration, requiring at least a microcontroller to calculate its *very* rough speed.
2. I assume that you Frisbee will be spinning? This brings the small matter of centri- forces acting on your accelerometer.

Overall, this would would make for a heavy Frisbee that is about as accurate as Microsoft's loading bar.

Maybe a GPS would be a better idea, the only downside is that it would be even heavier again. You might be able to achieve a positional accuracy of about 1 to 2 metres though, so you would have not throw it rather far to return a meaningful reading.

Any other ideas? I am interested was to what we can come up with.

 

[LazyBoy]

Hi and thank you for your super fast reply.

Sorry I did not explain my idea very well...I was thinking of the rotational speed in RPM.

I have Googled "battery powered bluetooth accelerometer" and it looks like you can get tiny units measuring about 20mm diameter x 5mm deep.

I am not sure of the weight but they do not look like they would weigh too much.

 

[Anon_LG]

OK, rotational speed is realistic.

I found this, on the link between centripetal acceleration and rotation. A little confusing, but workable. Alternatively, if boring algebra is not wanted, the Frisbee could be fitted with the accelerometer and spun at a variety of known speeds. This would not provide a reading that was particularly close to the value but it is an option.

Which would you prefer? If you went for the first option, you need to know the position of the accelerometer. If we went for the second one, then approximately 20 readings could be taken, 1 rotation per second extra each time etc. And record the outward acceleration each time.

 

[LazyBoy]

Thanks again...very interesting and helpful.

I would go with the first option and fit the accelerometer dead centre of the Frisbee for accuracy and best balance etc...

Should the RPM be based on the outside edge (total diameter) of the Frisbee?

 

[Anon_LG]

Ah, unfortunately I think that you need to look at the cenripetal acceleration equation. r will refer to the radius of the circle that the accelerometer makes on its circular path and v the velocity of the same. So positioning the accelerometer dead centre would not yield a reading. You could however position the accelerometer very near to the centre. Measure the distance from the accelerometer to the centre of the Frisbee, this is r. W = 2pi f, so a = (2pi f)^2 * r. I will probably be on tomorrow to clear this up and re-arrange. I hope my algebra is alright.

I will follow this through to completion. I hope this helps,

 

[BobK]

You don't need the equation. An accelerometer configured to read the acceleration tangential to the rotation would put out a sine wave at the frequency of rotation. All you would need to do is measure that frequency, and it would be very accurate.

Bob

 

[hevans1944]

I would fit two small transmitters of slightly different crystal-controlled frequencies to opposite outer edges of the Frisbee and try to measure the Doppler shifts. Probably need to do some maths at the receiver on the two Doppler shifted frequencies to get RPM, but you would also have data coming in on velocity. What with batteries and time of flight limitations, a powered Frisbee might be more practical... do such things really even exist?

 

[LazyBoy]

Thanks guys...I will let you know how I get on...

 

[(*steve*)]

An accelerometer configured to read the acceleration tangential to the rotation would put out a sine wave at the frequency of rotation.

I'm sad to say that I had to think about that for a moment.

 

[Colin Mitchell]

I would take a video and slow it down and read the RPM.

 

[Anon_LG]

You don't need the equation. An accelerometer configured to read the acceleration tangential to the rotation would put out a sine wave at the frequency of rotation. All you would need to do is measure that frequency, and it would be very accurate.

But surely a Frisbee with constant linear motion through space would encounter the same centripetal force as one not moving at all? If the frisbee's linear movement involved no acceleration, then there are no other forces to disturb the rotational motion causing a constant centripetal outward force.

Please explain, this is very confusing and interesting.

Lazyboy, use bob's method, it sounds as though he knows quite a bit about this area.

 

[hevans1944]

... Lazyboy, use bob's method, it sounds as though he knows quite a bit about this area.

No, @LazyBoy, use my method! It's a lot more complicated and requires sophisticated electronics and software processing. Where's the fun in doing it @BobK's eminently practical way?!

 

[Anon_LG]

No, @LazyBoy, use my method!

Doppler shift does sound exciting, use all of the methods! Also measure the position of the Frisbee by bouncing laser beams off of quadcopters in the vicinity and triangulate.

And here is the re-arranged equation, if it is still worth anything. Just to clear thing up, this is for an accelerometer with the measuring axis at a right andle to the centre of the Frisbee.

a = (2pi f)^2 * r

a = 4 * pi^2 * f^2 * r

Sqrt(a) = 2 * Pi * f * sqrt(r)

Sqrt(a) / (sqrt(r) * 2 * pi) = f

So, square root the acceleration and divide by (the square root of the radius, times by 2, times by pi), and you have the frequency of rotation.

The axis you are measuring along is outwards, is, at a right angle to the center.

You are actually measuring the forces opposite to the one displayed above, but it is equal and opposite, making it equally valid.

 

[BobK]

I'm sad to say that I had to think about that for a moment.

No, don't be sad, because it does not work.

I was thinking of the sensor being in the same orientation throughout the revolution, but it is not, it rotates with the Frisbee. So the acceleration would actually read 0 at all times.

I posted without thinking it through all the way.

Bob

 

[(*steve*)]

No, don't be sad, because it does not work.

No, I think it would. But it would have to be off centre and pointing tangentially to the direction of rotation.

 

[hevans1944]

Think of the video images of astronaut trainees in the centrifuge, how the acceleration distorts their faces. Just substitute an accelerometer for the faces. Of course that doesn't provide rotation speed directly, but it does allow you to calculate it (probably).

Anyone up for calculating the Doppler shift for Bluetooth transmitter rotating at, say, 500 RPM?

 

[LazyBoy]

Sorry guys this is all a bit over my head...are you saying that an accelerometer can not measure the rotational speed and that I will need a gyroscope?

 

[(*steve*)]

Well there's debate about it.

I've just come up with an even easier method. All you need is a photodiode and to record or transmit the light intensity it sees either continuously or at at regular (and known) intervals.

get that data stream, do a little Fourier analysis and you should see a significant spike in the frequency domain at the speed of rotation.

 

[BobK]

I think it is over all of our collective heads.

On third though, I though Steve might be right, but for a different reason than I originally was thinking of.

Consider the Frisbee to be a uniform disc (or at least radially symmetric). When rotatating, any point on the disc, other than the center will be traveling in a perfect circle. For such motion, the tangential speed will be constant, and the only acceleration is in the direction from the point to the center. So a tangential accelerometer would read zero, except for the effect of the slowing of the rotation due to friction.

That was my second thought.

My third thought, after Steve's 2 posts, was this. The accelerometer is going to have some mass. So it would make the disc non-uniform and introduce a wobble in the rotation. The tangential accelerometer would pick up this wobble and it would be sinusoidal.

BUT, now I am on my fourth thought. How can disc wobble without any forces to change it's motion? We are all familiar with rotating things that wobble when they are not balanced, notably the wheels on our cars and ceiling fans. But there is a difference between these and a Frisbee. These wobbling things are tied to an axle. The non-uniform mass distribution simply changes the natural center of rotation away from the axle and it provides the forces to wobble, indeed, if you look at your ceiling fan, the down tube wobbles in a circle. In the case of the Frisbee, with no axle, the center of rotation simply changes, and there is no wobble. Points on the rim will make circles of different sizes, but will still travel in circles.

Isn't Physics fun?

Any fifth thought?

Bob