As I've mentioned in an earlier post, I have been working on a digital-to-analog converter that will enable me to "drive" a mechanical Smiths centre speedo. In order for the whole thing to work I need to accurately convert the digital output from the R1 engine to a RPM (revolution per minute) factor that turns the mechanical cable.
Here are the maths I have been working on. These might not be accurate and I will hopefully receive the DC motor soon so I can test it all out.
Front Sprocket = 14 tooth
Rear Sprocket = 41 tooth
1 mile = 63360 inches
Smiths Speedometer TPM (Turns Per Mile) 1248
Wheel circumference based on tyre size;
Calculating number of pulses per mile;
1. Gear Ratio = Driven Gear / Driver Gear = 41/14 = 2.928571429
2. Gear Inches = Wheel Circumference x Driver Gear / Driven Gear = 19.1 x 14 /41 = 6.52195122
3. Inches traveled per Wheel Rev = Gear Inches x 3.14 (pi) = 6.52195122 x 3.14 = 20.478926831
4. Wheel Revs per Mile = 63,360 / 20.478926831 = 3093.912123563
5. VSS Pulses per Rev of 14 tooth = ?
6. VSS Pulses per Mile = 3093.912123563 x ? =
As you can see I do not know how many pulses are created per revolution of the R1 crank so I have written an Arduino sketch that will count them. I will need to carry out this test once I have the engine in a position to apply power unless I can find a definitive answer online. I have read 28 somewhere and 34!
Smiths RPM factor;
My Smiths speedometer requires 1248 Turns Per Mile to be accurate. I know this because 1248 TPM is written on the face of the dial. There is a very detailed guide on how to calculate the TPM over on Guessworks website.
1248 TPM means my drive cable will be turning at 1248 RPM (Revolutions Per Minute) at 60 mph. The RPM factor (that's what I am calling it) is;
1248 / 60 = 20.8
So if the speedometer drive cable is turning at 20.8 RPM the dial will register 1mph and every 20.8 RPM increase will result in a 1mph increase. I have plotted this on a spread sheet to show the required number of RPM for every mph up to 120mph.
In other words RPM = Speed x 20.8
The RPM values will be the required output of the DC motor driving the speedometer cable. I will be using PWM (Pulse Width Modulation) to accurately adjust the RPM output of the DC motor for the desired speed.
Based on my spread sheet I know that 2496 RPM equates to 120mph so I pruchased a 10V 2700 RPM DC motor. I will more than likely power it at 9v so the max RPM will be reduced closer to the 2496 max I require. In reality my Smiths speedometer max's out at 100mph and I don't plan on breaking the speed limit anyway :-)