Math Q: Wheel size vs speedo

[leafspring]

My recently purchased 04 plate Ignis sport is wearing 195/45-R16s on aftermarket 16 inch rims of unknown manufacture (not for much longer I hope) AFAIK They should be 195/50-R15.

I know the width correct (meaning the track, castor and camber angles are virtually un-affected) but I'm not sure about the rolling circumference...

So until I source OE/the correct size replacement wheels, how far out is my speedo reading and in what direction? (if at all)

I'm assuming it's reading slow, as the larger wheel travels that little bit further over the time of one rotation... given that D x T = S

[calibrax]

http://www.miata.net/garage/tirecalc.html

Your speedo will appear 1% too slow, i.e. when your speedo shows 60mph, your actual speed will be 60.6mph (of course, that assumes your speedo is 100% accurate, when the reality is that the speedo usually shows higher than your actual speed by a few mph)

Edited by calibrax on Sunday 25th May 18:46

[kambites]

The overall rolling circumference of a tyre is: diameter in mm ((inches * 2.54) + (profile/100 * width)) * 2 * pi

195/50/15 = (15 * 25.4 + 50/100 * 195) * 2 * pi = 3006.5 mm
195/45/16 = (16 * 25.4 + 45/100 * 195) * 2 * pi = 3104.8 mm

They differ by around 3%.

[leafspring]

So I'm going roughly 5% faster than the speedo says then?... officer

Ok

[kambites]

It's well within the margin of error that tends to be built into modern speedos anyway.