# Maths is cool - Part 3by Steve Smith

The following case study tripped me up numerous times, so I thought it would be a good time to revisit how to graph road speed via the ABS speed sensor signal:

Case study – Subaru with incorrect ABS operation

Using a math channel to calculate the road speed from an ABS wheel speed signal can be very useful when faced with this kind of diagnosis or if you need to qualify vehicle speeds against serial data.

With a tyre size of 215 x 45 17 and an ABS pole/tooth count of 48, we have:

• Number of teeth or pole count at the ABS pickup ring – physical count = 48
• Tyre circumference = diameter (0.625 m) * π (3.14)
• The number of wheel/tyre revolutions in one minute = 60/48 poles*signal frequency

The formula for wheel speed in miles per hour is:

• Wheel/tyre speed (frequency Hz*60 = RPM)*Tyre circumference (meters) = meters per minute
• Meters per minute*60 = meters per hour
• Meters per hour/1000 = kilometres per hour
• Kilometres per hour*0.621371 = miles per hour

The formula required to calculate miles per hour from the wheel speed signal on Channel B is: 60/48*freq(B)*(3,14*0.625)*60/1000*0.621371

To create a math channel to calculate mph for the wheel speed signal on Channel B, open the Math Channel Wizard by clicking on 'Tools > Math Channels > Create > Next > Advanced', and type in the formula above. Follow the Math Channel Wizard, selecting a colour, measurement unit (mph) and range for the math channel. To make it easier to recognise the math channel you created, select a matching colour for the channel input that is to be graphed.

The image below highlights the math channel formula entry procedure. Perhaps you require kilometres per hour as the road speed unit. Assuming that the ABS signal is on Channel A, the ABS pickup has 48 teeth and the tyre size is 215 x 45 17 the formula is as follows: 60/48*freq(A)*3.14*0.625)*60/1000

The .psdata file below has the math channels for mph in red and blue, the math channel for km/h is in magenta. 