# MOI and Angular Acceleration

• Ignyte
In summary, the conversation is about a large steel drum that has a laser cut disk on the end and a sensor that measures the "delay" of the drum. When the drum rotates, the sensor can measure the "delay" of the drum, either on or off. The problem is that they are struggling to get the power output to match correctly. They are using gnuplot to make a graph of the saved data, and one of their firmware outputs human readable information with a bunch of stuff. One of the things it says is that the RPM is matched to the engine rpm when the bike is reved to 12000rpm. They are also struggling to get the power output to match correctly because math is not really their strong suit
Ignyte
This may be a weird one, so please hang in there with me on this.

I have a large steel drum, its ~450kg. Measured to be 11.83kg/m^2 for its rotational inertia. (MOI).

On the end of it we have a VERY accurate laser cut disk. Has 4 teeth, 4 gaps. Equally spaced and all the same "delay".

When we rotate the drum we have an optical sensor which can measure the "delay" of its state, either on or off. Measurement is down to microsec's. So that's accurate enough for us. As the drum speeds up in rotation, the delay becomes shorter.

What we are struggling with is Angular Acceleration. Basically we need a way to tie all this together.
As for the actual practical application of this, think of a motorcycle dyno. As that what it actually is. I can provide pictures if so required.

We have some sample data recorded and so far we have had limited success.

We got the bike to 4000rpm, and held it and "calibrated" the drum rpm. Then as the bike increased or decreased rpm in that set gear, it perfectly showed what the engine was doing. So reving the bike to 12000rpm the dyno drum said "engine should be at 12000rpm" and it matched perfectly. We tried in several spots and also one "run".

We are struggling to get the power output to match correctly because math is not really our strong suit.
I have sample (open source) firmware for our hardware (teensy++, basically arduino) and some recorded data of one of the runs for analysis.

If someone can help me with what we may be doing wrong it would be GREATLY appreciated.

We are using gnuplot to make a graph of the saved data.

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EDIT
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Ill add how we are going about it, if it helps any..
We are measuring 2 samples. On and off, and measuring them in microsec. These numbers are written to the .dat file. They are currently written in hex (ascii) but that's non trivial to do it any way we choose.
xxxx,yyyy
xxxx,yyyy
etc.
One of our firmware outputs human readable info with a bunch of stuff.. here's a snip:
Code:
Received nothing (Tooth #1) from Drum, timed out (seconds): 10
RPM: 153.72   KM/H: 13.15   Tooth 1: 97.58ms   Tooth 2: 82.71ms
Difference: +14.87ms (Drum Speeding UP)
RPM: 196.24   KM/H: 16.79   Tooth 1: 76.44ms   Tooth 2: 68.96ms
Difference: +7.48ms (Drum Speeding UP)
RPM: 240.22   KM/H: 20.56   Tooth 1: 62.44ms   Tooth 2: 58.13ms
Difference: +4.32ms (Drum Speeding UP)
RPM: 272.56   KM/H: 23.32   Tooth 1: 55.03ms   Tooth 2: 51.57ms
Difference: +3.47ms (Drum Speeding UP)
RPM: 307.57   KM/H: 26.32   Tooth 1: 48.77ms   Tooth 2: 47.44ms
Difference: +1.33ms (Drum Speeding UP)
RPM: 321.64   KM/H: 27.52   Tooth 1: 46.64ms   Tooth 2: 44.87ms
Difference: +1.77ms (Drum Speeding UP)
As an example:
sample1 = 20750microseconds, sample2 = 20194 microseconds

We can then figure out:
rpm1 = (60000 / ((sample1 / 1000) * 4))
rpm2 = (60000 / ((sample2 / 1000) * 4))

rpm1 = 722.89
rpm2 = 742.7
rpm_gain = (742.7 - 722.89) == 19.81 rpm
angular_velocity = (20750/60) * (2*pi) == 79.79 rad/s
angular_acceleration = (79.79 / 2.074) == 41.424 rad/s2
torque = (11.83 * 41.424) == 429.667 Newton metres
power = (429.667 * 722.89) / 9549) == 32.527 kilowatts

Is all this right, or are we way off the mark ?

Last edited:
Hi Ignyte, I'm building a Inertia Dyno too, but I use a PIC16f876 and a hall effect sensor, and send the time of each revolution of drum to the PC through serial port.
I programming in Visual Studio C# 2010, and I create a softwar that calculates the power and torque.
Now you dyno is working?

If you want more information, send me a PM and I give you my email.

Regards,
Enzo.
From Argentina.

## 1. What is MOI and how is it related to angular acceleration?

MOI stands for moment of inertia, which is a measure of an object's resistance to rotational motion. It is related to angular acceleration because it determines how quickly an object will rotate when a torque is applied to it. The larger the MOI, the slower the object will accelerate, and vice versa.

## 2. How is MOI calculated?

MOI is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation. Mathematically, it is represented as I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

## 3. What factors affect MOI?

The main factor that affects MOI is the distribution of mass in an object. Objects with more mass concentrated towards the axis of rotation will have a lower MOI, while objects with more mass distributed away from the axis of rotation will have a higher MOI. The shape and size of an object also play a role in determining its MOI.

## 4. How does angular acceleration affect an object's motion?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is directly proportional to the applied torque and inversely proportional to the object's MOI. A larger angular acceleration will cause an object to rotate faster, while a smaller angular acceleration will result in slower rotation.

## 5. How can MOI and angular acceleration be applied in real-world situations?

MOI and angular acceleration are important concepts in physics and engineering, and they have many practical applications. For example, they are used in designing and analyzing the motion of objects such as satellites, airplanes, and vehicles. They are also crucial in sports such as gymnastics, figure skating, and diving, where understanding and controlling rotational motion is essential for performing complex movements.

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