Some maths help please

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B

Billybones

Active Member
Posts
79
Location
Kent
Hi can anyone tell me what percentage is a 265/75-16 tyre taller than a 255/70-16 tyre please.
Thank you Bill.
 
I've discovered you can't easily type out calculations in a standard post. So, I've set it out in Word with a few text boxes, took a screen shot, saved it, cropped it, saved it again and then posted it it as an image.
maths.jpg

Having done all of that, can I ask why you want to know :confused: :)
 
That gives the percentage increase in the aspect ratio, but doesn't allow for the tyres being of different widths. The percentage increase in rolling diameter or circumference of the new (n) versus the old (o) tyres is as follows:

upload_2021-11-9_8-57-48.png


Width and wheel size must both be in the same units - inches or mm. In this case:

upload_2021-11-9_8-59-18.png
 
Thank you for all your reply's and hard work :).
The reason for the question is that i am changing tyre size from the 255s to the 265s and i know this will put my speedo and odometer out, another member on this site has said that if i go bigger than a certain % i could have other problems so i wanted to know by what % i was going taller, also it will help by giving me an idea of how far out my speedo will be.
Hope this makes sense ??.
Bill
 
Billybones said:
Thank you for all your reply's and hard work :).
The reason for the question is that i am changing tyre size from the 255s to the 265s and i know this will put my speedo and odometer out, another member on this site has said that if i go bigger than a certain % i could have other problems so i wanted to know by what % i was going taller, also it will help by giving me an idea of how far out my speedo will be.
Hope this makes sense ??.
Bill
Click to expand...
Ahh, but that's not what you originally asked :p
I guessed it was something to do with wheel arch clearance. As usual, @neilly was thinking along the right lines :rolleyes:

As far as I know your speedo will be affected by the diameter of your wheel and tyre combo as this affects the circumference and so the number of revolutions the wheels do over a certain distance and time.

So, the % increase in overall diameter.
Maths b.jpg

To calculate the circumference we multiply both circumferences by the constant π (Pi) Multiplying everything by the same constant increases everything in the same proportion and so should work out the same.
So, comparing circumferences.
Maths c.jpg


To double check.
Maths d.jpg


However, I wouldn't be bothering with all of that b@ll@cks. I would use a sat nav to check your speedo. They're very accurate.

You might need to adjust your steering lock stop bolts as the bigger tyres may well hit your radius arms as you approach full lock.
 
I see where the discrepancy is now. '70' in 255/70-16 isn't 70mm, it is the aspect ratio i.e. the height of the sidewall as a percentage of the tyre width - 70%. For the original tyre that would be 255 x 70 / 100 = 179mm. For the new tyre it is 265 x 75 / 100 = 199mm. Substitute these figures into your calculations and we get the same results.
 
Ah, so only about 2% difference then ,think i can live with that, sat nav not really practical as it was more about working out fuel consumption than speed.
Agree with what you say about lockstops but think i might have to use spacers as already got the shorter of the two bolt lengths that was fitted to a D2 and the 255 tyres already rub on the radius arms but the longer ones give me the turning circle of a small oil tanker :(.
Thanks for the help, Bill
 
Al2O3 said:
Ahh, but that's not what you originally asked :p
I guessed it was something to do with wheel arch clearance. As usual, @neilly was thinking along the right lines :rolleyes:

As far as I know your speedo will be affected by the diameter of your wheel and tyre combo as this affects the circumference and so the number of revolutions the wheels do over a certain distance and time.

So, the % increase in overall diameter.
View attachment 252346
To calculate the circumference we multiply both circumferences by the constant π (Pi) Multiplying everything by the same constant increases everything in the same proportion and so should work out the same.
So, comparing circumferences.
View attachment 252347

To double check.
View attachment 252348

However, I wouldn't be bothering with all of that b@ll@cks. I would use a sat nav to check your speedo. They're very accurate.

You might need to adjust your steering lock stop bolts as the bigger tyres may well hit your radius arms as you approach full lock.
Click to expand...

Your maths is a little out there matey.

the 70 is the % of the width. It is still a tad over 5 %.
@Billybones
Your speedo will measure 5% under.

Cheers
 
Keith_L said:
I see where the discrepancy is now. '70' in 255/70-16 isn't 70mm, it is the aspect ratio i.e. the height of the sidewall as a percentage of the tyre width - 70%. For the original tyre that would be 255 x 70 / 100 = 179mm. For the new tyre it is 265 x 75 / 100 = 199mm. Substitute these figures into your calculations and we get the same results.
Click to expand...
So isn't the difference in profiles 199 - 179 = 20mm.
(20 x 100)/179 = 11% more than a 255 x 70 tyre.
At top and bottom of wheel too so thats 22% or 40mm diameter increase.
 
The depth of the sidewall is 11% greater and the difference in the diameter is 40mm as you say, but to calculate the percentage increase in the rolling diameter (or circumference), which is what will impact the speedometer, you need to include the 16" / 406mm wheel. The difference then becomes 804mm vs 763mm. 804 / 763 = 1.053 i.e. 5.3% bigger.
 
Keith_L said:
The depth of the sidewall is 11% greater and the difference in the diameter is 40mm as you say, but to calculate the percentage increase in the rolling diameter (or circumference), which is what will impact the speedometer, you need to include the 16" / 406mm wheel. The difference then becomes 804mm vs 763mm. 804 / 763 = 1.053 i.e. 5.3% bigger.
Click to expand...
Simplest way, take a piece of chalk, mark the tyre and the floor where both touch it, then roll it forward until the chalkmark on the tyre touches the floor again. continue the mark onto the floor. The distance between the two is the rolling circumference. BUT, if you are going fast enough the tyre may well swell a tiny bit with the heat and the circumference may change as centripetal force throws it out a bit too.
In the end it is a science but not that exact a science. As long as the speedo doesn't under-read......
 
Keith_L said:
The depth of the sidewall is 11% greater and the difference in the diameter is 40mm as you say, but to calculate the percentage increase in the rolling diameter (or circumference), which is what will impact the speedometer, you need to include the 16" / 406mm wheel. The difference then becomes 804mm vs 763mm. 804 / 763 = 1.053 i.e. 5.3% bigger.
Click to expand...
You haven't been around long enough to know this. I have, so it's all my fault :( @neilly is always right. :cool:
However, we can console ourselves by remembering that 'nobody likes a smart @rse'. ;)
 
Al2O3 said:
You haven't been around long enough to know this. I have, so it's all my fault :( @neilly is always right. :cool:
However, we can console ourselves by remembering that 'nobody likes a smart @rse'. ;)
Click to expand...

I never said @Keith_L was wrong, in fact I thought his response was quite correct , post #6.

So I was not a smart @rse with his response, just said yours was slightly wrong. Sorry of you thought that was being a smart @arse, However....

Marjon had already supplied a link to the tire calculator. To determine the hight and the circumference. Which the OP and anybody else not capable of working it out correctly could have used and received an approximate reply. Post #2.


Cheers
 
neilly said:
I never said @Keith_L was wrong, in fact I thought his response was quite correct , post #6.

So I was not a smart @rse with his response, just said yours was slightly wrong. Sorry of you thought that was being a smart @arse, However....
Click to expand...
I thought he was calling me a smart @rse, not you, on the basis you are a long serving member of the Forum and have earned the right to correct him, whereas I'm just a newbie. :)
 
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