Alloy Maths

[Niraj]

As you all know, I have an inquisitive mind, and I have my own answer to this, so I'm hoping for some good answers here...

Just trying to get technical for a bit...

Background Information

~~~~~~~~~~~~~~~~

A 13" steel wheel, has a 175/70/13 tyre installed.

A 17" alloy rim, has a 215/40/17 tyre installed.

A set of 13" wheels are fitted to a vehicle and driven down a road.

A set of 17" rims are fitted to an identical vehicle and driven down the same road.

The 13" wheels are fitted by manufacturer and the speedometer is calibrated to those sized wheels.

The Question

~~~~~~~~

1. If both vehicles are travelling at 70mph indicated by the speedo. Which car is physically moving faster?

2. If so, by how much?

3. What is the real speed difference between both sets of wheels at the indicated speedometer reading of 100mph?

Let me offer some more information...

1" = 25.4mm

13" steel wheel = 330.2mm

175/70/13 tyre = 70% the width of the tyre ?? or 70% of the diameter of the rim?

Circumference of circle = 2Πr

Π = 22/7

Hint

~~~

Work out each circumference of the wheel and the alloy, find the difference, and understand how much further the wheel/alloy may travel over the other.

I know this is really boring! but give it ago, maybe we'll all amaze ourselves!

[MacRS200]

You don't actually have to go as far as working out the circumference, the proportional difference between the diameters is the same as the that of the circumferences :winky:

The alloy is approx 5% bigger than the steel and so travels 5% further than the steel in 1 rev, so answers are:-

1/ Alloy

2/ 3.5 MPH

3/ 5 MPH

[Niraj]

You don't actually have to go as far as working out the circumference, the proportional difference between the diameters is the same as the that of the circumferences :winky:

Correct with reference to proportional difference :D but you must show your working out... :P

The alloy is approx 5% bigger than the steel and so travels 5% further than the steel in 1 rev, so answers are:-

1/ Alloy

2/ 3.5 MPH

3/ 5 MPH

[MacRS200]

(13 x 25.4) + (2 x (175 x 0.7)) = 575.2

(17 x 25.4) + (2 x (215 x 0.4)) = 603.8

Difference = 603.8 - 575.2 = 28.6

(28.6 / 575.2) * 100 = 4.9%

2/ 70 x 1.05 = 73.5

3/ 100 x 1.05 = 105

Do I get a gold star now teach

[Niraj]

MacRS200 receives 3 points.

The games will continue :D

On a different note, (for others) this is the way in which you can calculate the error in your speedometer if you change your wheels.

Additionally, you can use reverse mathematics to figure out which tyre you can use on your alloy, to be as close to the best Speedo reading as possible

:D

[Niraj]

NB:

For the above scenario, the driver with 17" rims or bigger with a stock rim of 13", must be extra careful when driving through 50mph zones with speed cameras!

Driving at 48mph (speedometer) could result in getting a speeding ticket!

[DJ Wozza]

"must show your working out" PMSL

sounds far too much like Skool to me

[MacRS200]

NB:

For the above scenario, the driver with 17" rims or bigger with a stock rim of 13", must be extra careful when driving through 50mph zones with speed cameras!

Driving at 48mph (speedometer) could result in getting a speeding ticket!

Don't think that 50.4 MPH would get you a ticket :D

48 * 1.05 = 50.4

But you do have a point mate,

[Rikos]

You have far too much time on your hands

[Niraj]

You have far too much time on your hands

You're the 3rd person to say this to me today :(

Time is the one thing i dont have enough of !!! honest

[derekyau]

NB:

For the above scenario, the driver with 17" rims or bigger with a stock rim of 13", must be extra careful when driving through 50mph zones with speed cameras!

Driving at 48mph (speedometer) could result in getting a speeding ticket!

Blah blah blah.

who the hell would have a car with 13" rims anyway...

:shutit:

[Rikos]

I think it's CV's next mod :P

I'm sorry i broke!!

[RX-Men-8]

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

[WylieCoyote]

It's amazing what deep analytical and scientific concepts one ponders when boredom kicks in lol! That thought would simply have never occured to me but it's a fair comment about what's displayed on the speedo and what the car is actually doing. That'll keep the old grey matter working for a day or so!

Keith