Tire sizes in GPB

[HornetMaX]

Hi all,
there's some confusion on how GPB models the tire sizes, so let's try to write here what (I think) we know. Would be nice to have a confirmation all this is correct.
I won't discuss all the other parameters as many of them I do not have a 100% accurate idea of what they do, so here we'll look only at the ones at the end of the .tyre file (here from the 990 rear) and related to the tire dimensions:

Code Select Expand

Radius = 0.325
TorusRadius = 0.13
Width = 60

Radius is the overall radius (from rim center to radially farthest point on the tire tread), in meters. It's not the rim radius.
It is measured with the wheel suspended (otherwise the weight will compress the tire) and not rotating (at high speeds, the tire tends to "balloon" due to centrifugal forces, increasing the radius).

Torus radius: GPB describes the tire shape (or profile) as a torus (donut, for our american friends). This means that you can't have any profile you want (more or less V shaped), it's just a torus. It indicates the torus radius in meters. On this page (http://en.wikipedia.org/wiki/Torus) it would be the "r" (lowercase r) in the 3 equations under the Geometry paragraph.

Width = this is in degrees and it's the unusual thing. It defines the circle sector that describes the tire tread. In this image you have the cross section (one of the two, actually) of our torus/donut:

r is our TorusRadius, Theta is 2 x Width. For Width = 0 you have ... hmm ... a thin tire (just a conceptual thing), for Width = 90 (Theta is 180) you have the whole semicircle.

Usually tire dimensions are presented as 195/55ZR-17: 195 is the tire width in mm (the length of the horizontal line in the figure above), 55 is the relative height of the tire shoulder (55 means the shoulder is 55% of the width, in this case the shoulder is .55*195 = 107.25mm), Z is the speed rating (we don't care), R for Radial (we don't care) and 17 is the rim diameter in inches (hello, non-metric people !).

So how do we go from GPB parameters (Radius, TorusRadius and Width in degrees) to "real life" parameters (e.g. 195/55ZR-17) and vice versa ?

Real life -> GPB:

• 17 inches = 43.18cm = 431.8mm rim diameter ==> rim radius = 215.9mm
• Tire shoulder = 0.55 * 195 = 107.25mm
• Total (rim + tire) radius = rim radius + tire shoulder = 215.9 + 107.25 = 323.15 : that's GPB's Radius.
• For TorusRadius and Width (in degrees) we have to find two values such that 2 * TorusRadius * sin(Width) = 195mm. There're multiple solutions but, unless you can measure these from a real tire, you can assume Width to be 60 and hence compute TorusRadius as 195mm / (2 * sin(60)) = 113mm = 0.113 in GPB

GPB -> real life for the 990:

• The Width in m is given by 2 * TorusRadius * sin(Width in degrees) = 2 * 0.13 * sin(60) = 0.225m = 225mm (that's my kind of rear tire !)
• The rim diameter and tire shoulder are not really used by GPB. If you assume the relative height of the shoulder to be 50, then you have the shoulder as 0.50 * 225 = 112.5mm, hence the rim radius will be 325 - 112.5= 212.5mm, so diameter is 425mm or 16.7 inches.

@neoraptor: your .ggb file here (http://gpbikes-mods.wikia.com/wiki/Tyres) is hence probably wrong, as it says that Radius in GPB is the rim radius.

MaX.

[C21]

Thank You 
The sin(60) was the issue i struggled....
You pic makes it more clear now.

e.g.
Varese rear tyre:
0,11 / 60 / 0,305
2*0,11*sin(60)= 0,1905m=190mm
0,50*190=95mm
305-95=210
420/25,4=16,53"

That leads me to the question:
Did they have 16,5" rims in the 2Stroke area?

BTW:
I will make a quick list for the GPB values for the usual tyre sizes.

[Hawk]

That leads me to the question:
Did they have 16,5" rims in the 2Stroke area?

I know that in the 2 stroke era they did use 16 inch rims at times, especially on the front and 17 in mainly on the rear.

[C21]

Yes in the old days they did that.
I mean the 2strokes inbetween 96-2001 

I will attach an Excel File in a few hours for the Tyres.

[HornetMaX]

Thank You 
The sin(60) was the issue i struggled....
You pic makes it more clear now.

e.g.
Varese rear tyre:
0,11 / 60 / 0,305
2*0,11*sin(60)= 0,1905m=190mm
0,50*190=95mm
305-95=210
420/25,4=16,53"

That leads me to the question:
Did they have 16,5" rims in the 2Stroke area?

I think 16.5 rims are more recent than that, before they had either 16 or 17.

However, notice that you have assumed 50% shoulder height, maybe it was 55 or something.

MaX.

[C21]

Nearly finsihed the excel sheet...maybe 40minutes...
Huge range of tyre sizes.... 

[BozoCRO]

Thank You 
The sin(60) was the issue i struggled....
You pic makes it more clear now.

e.g.
Varese rear tyre:
0,11 / 60 / 0,305
2*0,11*sin(60)= 0,1905m=190mm
0,50*190=95mm
305-95=210
420/25,4=16,53"

That leads me to the question:
Did they have 16,5" rims in the 2Stroke area?

I think 16.5 rims are more recent than that, before they had either 16 or 17.

However, notice that you have assumed 50% shoulder height, maybe it was 55 or something.

MaX.

16.5 made Garry McCoy famous. Bofore that everone used 17' rear

[C21]

Done.
You can DL as word(docx) or excel(xlsx).

Edit:
An Error Has Occurred!
The upload folder is full. Please try a smaller file and/or contact an administrator.

Strange, File size is 13 and 16kb...
Try this..
DL Link:
https://mega.co.nz/#F!LJdgxBoT!ZDiBSy_6T4J_guVyLbFijw

In my opinion the file is self explaining.
Highlighted MotoGP, Moto2 and Moto3 tyres. Only one size for each of the three classes based on FIM rules. Dunlop supplies Moto2 and Moto3 exclusivly and Bridgestone supplies MotoGP exclusivly.
For WSBK and WSSP, WSST Pirelli is the exclusiv supplier. But you have choices in Tyre size. Did not highlightend these sizes in the sheets. Pic 120/70 for front and 180/55, 190/55, 200/60 rear in 17" (only 17" allowed in 2014) or (allowed by rules up to 2013) pic 120/75R420 front and 190/65R420 rear for 16.5" Slick tyres.
If you´re on rain/wet Tyres pic also 120/70 front but 190/60-17 rear. For 16.5" rain/wet tyres pic same size for front as slick but 195/65R420 for rear tyre.

[HornetMaX]

Edit:
An Error Has Occurred!
The upload folder is full. Please try a smaller file and/or contact an administrator.

Strange, File size is 13 and 16kb...

Not sure, but it may be each user here has a quota he can use for attachments, maybe you've almost exceeded your one.
Got the same problem myself yesterday, but I've uploaded a few pics for the guide so ...

MaX.