My Stirling Engine: speed check

When I ran my engine for the first time, I couldn't believe how fast it was going.

 

Naturally I was curious.

So I had to build a simple tacho to check the speed.

This post follows on from: My Stirling Engine: assembly & run

As the flywheel has 3 spokes, I thought I'd try to use infrared diodes to deduce the number of revolutions per minute (rpm) by building a small tacho module either side of the flywheel.

Although I already had a number of iR diodes, I searched through all my 'man tins' but could not find a detector. And although I have a disused birdbox in the garage which I know has a diode/detector pair, I decided to buy some more.

I found that I could buy 20 components from Sourcing Map (10 x iR led & 10 x iR detector) for less than £7. They don't provide any component identities or useful electrical data, but that's not a show-stopper if you just want to experiment. So I knocked up a simple tacho using two resistors, an iR led, a iR detector diode, 6 AAA batteries and an old off-cut of vero-board.

 

tacho circuit

The resistor values are not super critical. With a 9 Volt battery, the current through the iR led is approximately:-

supply voltage - diode forward voltage / series resistor

I = (9 - 1.2)/0.47  mA 

= 17mA approx

This produces way more iR than I need, given that the iR led is less than 10mm from the detector. But it produces a very healthy 2.5V across the 10K detector resistor, so current through detector diode is:-

I = 2.5/10 mA

= 0.25mA = 250uA approx

I've no idea if this is a safe detector diode current, because I don't have a data sheet!

The tacho output is monitored using my Hantek USB 'scope module connected to my laptop.

measurements

The 'scope indicates a frequency of 50Hz (and therefore a waveform period of 20ms). But as there are 3 spokes on this flywheel, the rotational frequency is 50/3 = 16.67Hz (period = 60ms). And then, multiplying this by 60 seconds, gives us a rate of: 1000rpm

Although 1000rpm is only the tick-over speed on most petrol engines, it still seems fast for something that looks more like a steam engine.

But what about the piston in that heated cylinder, how fast is that moving?

Probably the best way to work this out is to consider a rotating vector. If you are not familiar with rotating vectors, imagine that there is a pencil attached to the edge of the flywheel, and that somehow it writes on a piece of paper as the engine runs.

If the paper is moving at a constant speed under the pencil, the plotted line will take the form of a sine wave.

 

The above illustration was created on a spreadsheet via OpenOffice Calc. The y axis values are calculated from:-

 Hot piston extension = (piston travel range/2) x Sin(Radians(vector angle))

The plot on the right represents the result of the vector (i.e the flywheel) rotating 180 degrees from the bottom position (-90') counter-clockwise to the top position (+90').

A point of clarification; turning the engine on its end might show more clearly the relationship with the piston con-rod and the vector above.

 

engine shown in the -90' position

The movement of the hot piston for this half cycle of flywheel rotation is 10mm (-5 to +5mm from the mid point). Remember that the time taken for one rotation of the flywheel was 60ms (the period of our 16.67Hz waveform). So one half rotation takes 30ms.

Therefore the average speed of the hot piston is:-

10mm/30ms = 0.333mm per ms

..or if I scale this I get:-

0.333 x 1000 metres/second

= 333m/s

...which is about the speed of a low velocity bullet or a lead pellet from a shotgun.

Taking this one stage further, its clear just by looking at the above plot that the piston is moving faster as the vector crosses the 0 degree line (this is basically the mid-way point for the piston).

Taking the data from my spreadsheet for the piston moving about the mid-way point by +/-9 degrees (18 degrees in total) I get about 1.56434465mm. Since 18 degrees are one tenth of 180, I get:-

peak piston speed = 1.56434465mm / (30ms/10)

= 0.521448217mm per ms

..or, if I scale up:-

521metres/second

 

So let's hope the piston never breaks free and hits me between the eyes!