Hi Russell2002,
I hope you find the following answer meets your needs. If not, please
request a clarification and I will address any problems or concerns
you have.
There is extensive math that I have included for your interest, but if
you don't care to see it, the results are summarized as follows. Note
that these results involve some simplifications and approximations and
are not meant to be exact (details about the nature of the
simplifications is at the beginning of the justification section
below).
275/40/18 tyres at a pressure of 35psi hold as much air
as 275/35/18's at 43.5psi.
245/45/18 tyres at a pressure of 35psi hold as much air
as 245/40/18's at 42.2psi.
Justification below:
We will idealize the situation slightly to make calculations easier.
Let's assume that the tyres are perfectly cylindrical and that the
sidewalls are perpendicular to the tread, etc. The resulting volumes
and pressures will not be off from the actual answers by more than a
couple of percent. Also note that the measurements neglect the
thickness of the rubber; this causes us to overestimate the volume of
the tyre, but our ignoring the bulging at the sidewalls and the volume
of the rim causes us to underestimate the volume of the tyre, so the
combination of the two factors will not cause our estimate to be -too-
far astray.
Decoding the tyre sizes, we seek information on the following four
sizes:
275/40/18:
Tread width 275mm, sidewall height 110mm, inside diameter 18
inches=457.2mm
245/45/18:
Tread width 245mm, sidewall height 110.25mm, inside diameter 457.2mm
275/35/18:
Tread width 275mm, sidewall height 96.25mm, inside diameter 457.2mm
245/40/18:
Tread width 245mm, sidewall height 98mm, inside diameter 457.2mm
So imagining the tyres as cylinders with holes in the center, we can
get their volume thusly:
Volume of whole cylinder - volume of hole = volume of tyre.
We will work in meters since this will make the numbers easier to work
with:
The volume formula for a cylinder is pi*radius squared*height, where
height in this case is the tread width, radius is the radius of the
tyre, and pi = approximately 3.1415926...
Volume of whole cylinders:
275/40/18: pi * .3386^2 * .275 = .0991 cubic meters
245/45/18: pi * .33885^2 * .245 = .0884 cubic meters
275/35/18: pi * .32485^2 * .275 = .0912 cubic meters
245/40/18: pi * .3266^2 * .245 = .0922 cubic meters
Now from each of these volumes we must take away the volume of the
hole in the middle, which for the tyres of 275mm tread width is .0451
cubic meters and for the tyres of 245mm width is .0402 cubic meters.
This gives the volume of the four tyres as
275/40/18: .0539 cubic meters
245/45/18: .0480 cubic meters
275/35/18: .0460 cubic meters
245/40/18: .0419 cubic meters
Now, using the Ideal Gas Law, we will be able to determine how much
air is in 275/40's and the 245/45's, and then work backwards and find
what the resulting pressure will be in the other tyres given the same
volume of air.
The ideal gas law tells us that if temperature and total amount of air
stay the same, there is an inverse relationship between pressure and
volume-- that is, the smaller the volume, the higher the pressure.
Specifically:
pressure * volume = a constant, for a given temperature and amount of
air.
(I am glossing over some details here.)
Using the convenient ideal gas law calculator at
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegasc.html#c1
we see that if the pressure reads 35psi at the gauge on the 275/40's,
the same volume of air in the 275/35's will produce a pressure reading
of 43.5psi on the gauge (assuming an ambient temperature of a balmy 25
degrees Celsius).
Likewise, the 245/45's at a pressure reading of 35psi hold the same
amount of air as the 245/40's at a pressure reading of 42.2psi.
(It is interesting to note here that as far as the gas law is
concerned, we need to take into account the nominal 14 psi that the
tire and gauge are both under due to the pressure of the atmosphere.
The gas law calculator takes this into account if you enter the psi in
the entry marked "gauge".)
To summarize:
275/40/18 tyres at a pressure of 35psi
hold as much air as 275/35/18's at 43.5psi.
245/45/18 tyres at a pressure of 35psi
hold as much air as 245/40/18's at 42.2psi.
I hope this answers your question satisfactorily. If not, please
request a clarification and I will do my best to answer more
completely!
Good luck,
smudgy.
Google search terms:
<tire dimensions>
Relevant results used for above:
http://www.tirerack.com/tires/tiretech/general/size.htm
<ideal gas law>
Relevant results:
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegasc.html#c1 |