cycling math question

[Bradford]

Because I took high school science, and because I'm not Roger Goodell, I know that my tire PSI will decrease as temperature decreases. However, since my math skills aren't great, I'm not sure I could figure out how much and get it right.

While commuting in the mid 20s the other day, it occurred to me that I inflate my tires the night before in a garage that is about 50 degrees, but ride in the morning in temps in the mid 20s, lets say 25 degrees. How much, assuming a 700 x 28 tire, would the PSI decrease just by going from 50 degrees to 25? Is it material, and if so, how much does it drop.

The temp on the ride home is usually back up around 50, so at least one half of the ride should be mostly unchanged.

[Dave]

This calculator says about 5 psi lower at 25.

http://physics.bu.edu/~schmaltz/deflate.html

Pressure is reduced by the ratio of T2/T1, with the temperature in degrees Kelvin.

https://www.google.com/search?q=absolute+temperature&oq=absolute&aqs=chrome.2.69i57j0l2j69i65j0.6990j0j8&client=tablet-android-samsung&sourceid=chrome-mobile&ie=UTF-8#imgrc=QcoXkiyQ7UaWjM:

[duff_duffy]

This will tell you everything you want to know:
http://flocycling.blogspot.com/2014/12/flo-cycling-tire-pressure-and.html?m=1

[MattTuck]

But if you ride fast enough, flex in the tire will generate heat. :banana:

[Louis]

But if you ride fast enough, flex in the tire will generate heat. :banana:

Plus there's the aerodynamic heating.

[Ken Robb]

Plus there's the aerodynamic heating.

This cracks me up!!:banana:

[OtayBW]

Please note: Tires/wheels will spin up faster at colder temperatures.
Thank-you.

[Bruce K]

Geez Bradford

I would have thought you would up to date on Boyle’s Law after Deflategate!

BK

[SlowPokePete]

Is there any change in how supple a tire becomes at colder temperatures and a way to quantify it ? :eek:



SPP

[old_fat_and_slow]

Use the "ideal gas law" which is:

Pv = MRt

pressure x volume = mass x universal gas law constant x temperature

Which means that as long as the volume is constant, the pressure will change linearly with the temperature.

[Louis]

Use the "ideal gas law" which is:

Pv = MRt

pressure x volume = mass x universal gas law constant x temperature

Which means that as long as the volume is constant, the pressure will change linearly with the temperature.

I thought it was PV = nRT (n = # of moles of gas)

[muz]

Please note: Tires/wheels will spin up faster at colder temperatures.
Thank-you.

I am guessing this was intended as a joke. Tires get stiffer at colder temperatures and tire friction losses increase.

[muz]

Use the "ideal gas law" which is:

Pv = MRt

pressure x volume = mass x universal gas law constant x temperature

Which means that as long as the volume is constant, the pressure will change linearly with the temperature.

And most importantly, the temperature is measured in degrees Kelvin. In our example, 50F=283K, 25F=269K. So the PSI would decrease by roughly 5%.

[martl]

There is a german commercial wheel builder who will explain in all sincerety, that a *wheels* stiffness actually changes due to temperature, because the aluminum rim will shrink/expand at a different rate than the steel spokes. (This is physically correct). He also claims it is *noticeable* by the rider, so, if you climb from Bourg d'Oisans to the top of the Iseran, the wheel will feel softer at the summit.

(I've ridden the Isearn but had always thought the thing feeling softer at reaching the summit were my legs..)

source (german language): http://www.radplan-delta.de/rennradtechnik/druckundtemp.html

[old_fat_and_slow]

Both variations are correct. (i.e., you can use "n" or "M".)


I thought it was PV = nRT (n = # of moles of gas)

[cderalow]

Both variations are correct. (i.e., you can use "n" or "M".)

the value of R varies between the use of n and M, they are equal, however have different units of measure.


for M it's 287 J/kg-K.

For n it's 8.314 J/mol-k

[jruhlen1980]

How much, assuming a 700 x 28 tire, would the PSI decrease just by going from 50 degrees to 25? Is it material, and if so, how much does it drop.

OK but if a person leaves Buffalo at 6:36 a.m. on Monday morning when the temperature is 25 degrees, traveling west at 17.6 mph with a 12 mph SSW headwind, and another rider on an ebike with disc brakes and tubeless tires leaves Denver at 12:29 p.m. the next Tuesday traveling east on only gravel roads and doesn't carry a frame pump, why do the ice cubes in the water bottle in my jersey pocket stay frozen longer than the ones in the bottle on my downtube?

[muz]

There is a german commercial wheel builder who will explain in all sincerety, that a *wheels* stiffness actually changes due to temperature, because the aluminum rim will shrink/expand at a different rate than the steel spokes. (This is physically correct). He also claims it is *noticeable* by the rider, so, if you climb from Bourg d'Oisans to the top of the Iseran, the wheel will feel softer at the summit.


Even if true, the effect would be extremely small. According to Jobst Brandt's "The Bicycle Wheel", stiffness of a properly tensioned wheel is largely independent of the spoke tension.

[93KgBike]

How are you measuring the temperature of the gas inside your tire?

[Jaybee]

the value of R varies between the use of n and M, they are equal, however have different units of measure.


for M it's 287 J/kg-K.

For n it's 8.314 J/mol-k


this is true. also note that for the problem in question, the value of n or M is constant, so the only thing changing is temp and pressure.

[Jaybee]

How are you measuring the temperature of the gas inside your tire?

For a non-rolling tire, I would generally assume that temp of the air inside is the same as the ambient air temp. so if you inflate in your 50F garage, it's with 50F air. In the morning, when you roll out, the T drops toward the ambient 25F, but probably doesn't get quite that low as friction and flex from the tire generate some heat.

Functionally, I'd be surprised if I could tell the difference while riding on most road tires. On a fatbike, even 0.5 psi change can be significant.

[dancinkozmo]

this thread makes me want to make the switch to solid rubber tires

[Jaybee]

this thread makes me want to make the switch to solid rubber tires


Material properties change with temperature as well. Everything is chemistry, can't avoid it.

:fight:

[dancinkozmo]

Material properties change with temperature as well. Everything is chemistry, can't avoid it.

:fight:

https://rlv.zcache.co.uk/funny_chemistry_teacher_quote_no_reaction_postcard-rf4872fee293747cbaf640617e0744679_vgbaq_8byvr_540. jpg

[martl]

Even if true, the effect would be extremely small. According to Jobst Brandt's "The Bicycle Wheel", stiffness of a properly tensioned wheel is largely independent of the spoke tension.

According to ye goode olde formula book, an aluminum part of length 2195mm (=rim) will shrink by 0.6 of a milimeter when brought from Bourg St Maurice (10°C) to the top of the Iseran (-5°C) (Temperatures as of today).
This results in a reduction of radius of 0.089 mm

A stainless steel spoke of l=300mm will shrink by 0.07mm only (effectively: a bit less, because if you're not using a radial spoke pattern, the spoke has an angle - but let'S not go there)

So we have a whooping 0.019 mm gap to cover. (For US automotive engineers: that is 1/10th of "sod it, we'll eyeball that")

That doesn't factor in the diameter and material of the hub, of course. It is fair to say that the effect will be more noticeable if you use low flange hubs...

[Bruce K]

All good info but the spoke is not free to contract.

It is in a system where it is already in tension and constrained by the rim resisting the contraction.

In all likelihood the temperature change would increase spike tension rather than the spoke actually shrinking. If they shrunk, the rim would get all wavy (not that you would notice the small amount).

The reality is the rim would probably deform marginally and the spoke tension would increase some as it is a system.

Makes for interesting conversation.

BK

[muz]

According to ye goode olde formula book, an aluminum part of length 2195mm (=rim) will shrink by 0.6 of a milimeter when brought from Bourg St Maurice (10°C) to the top of the Iseran (-5°C) (Temperatures as of today).
This results in a reduction of radius of 0.089 mm

A stainless steel spoke of l=300mm will shrink by 0.07mm only (effectively: a bit less, because if you're not using a radial spoke pattern, the spoke has an angle - but let'S not go there)

So we have a whooping 0.019 mm gap to cover. (For US automotive engineers: that is 1/10th of "sod it, we'll eyeball that")

That doesn't factor in the diameter and material of the hub, of course. It is fair to say that the effect will be more noticeable if you use low flange hubs...

Yes, I think we are almost at the answer. Let's assume that the rim doesn't appreciably deform, so the net effect is elongation or shrinking of the spoke. Let's also assume we remain on the linear portion of the stress-strain curve. We can then use Young's modulus to compute the change in strain on the spoke.

As a practical matter, I doubt it will change the stiffness of the wheel as a system. I mean, I can take a wheel and increase/decrease spoke tension, yet it will make little difference in how the wheel feels (may make a difference in fatigue resistance).

[oldpotatoe]

https://rlv.zcache.co.uk/funny_chemistry_teacher_quote_no_reaction_postcard-rf4872fee293747cbaf640617e0744679_vgbaq_8byvr_540. jpg

OK but if a person leaves Buffalo at 6:36 a.m. on Monday morning when the temperature is 25 degrees, traveling west at 17.6 mph with a 12 mph SSW headwind, and another rider on an ebike with disc brakes and tubeless tires leaves Denver at 12:29 p.m. the next Tuesday traveling east on only gravel roads and doesn't carry a frame pump, why do the ice cubes in the water bottle in my jersey pocket stay frozen longer than the ones in the bottle on my downtube?


:)

[martl]

Yes, I think we are almost at the answer. Let's assume that the rim doesn't appreciably deform, so the net effect is elongation or shrinking of the spoke. Let's also assume we remain on the linear portion of the stress-strain curve. We can then use Young's modulus to compute the change in strain on the spoke.

As a practical matter, I doubt it will change the stiffness of the wheel as a system. I mean, I can take a wheel and increase/decrease spoke tension, yet it will make little difference in how the wheel feels (may make a difference in fatigue resistance)

Agreed. Thread lead for a bicycle spoke thread is 0.45mm. We calculated Delta l as 0.019mm, and 450/19 equals 23.7 . We would need to tension each spoke by 15.2 Deg (1/23,7rd of a turn) for full compensation.

Come to think of it, the elevation difference also causes a slightly higher pressure difference of tire vs. atmosphere, which will compress the rim a bit more at the summit. So possibly a 15.5 Deg (or even 15.8 Deg ?) spoke tensioning may be required (bring your reading glasses)!

[Mark McM]

How are you measuring the temperature of the gas inside your tire?

Good point. When the air is compressed inside an air pump, it heats up. So when you inflate your tire, you're actually filling it with hot air. When the air in the tire cools back down to room temperature, it's pressure decreases. So the actual operating tire pressure will be lower than the initial inflation pressure.

Unless of course, you inflate your tires from a high pressure tank (at ambient temperature). In which case, the air cools as it expands when it fills the tire. In which case, the tire's operating pressure will increase as it warms to ambient pressure.

Which leads to the question: When will Silca introduce a new air pump with an integral intercooler, so that the pressurized air enters the tire at ambient temperature, for better control of tire operating pressure? No doubt, this pump will be made from titanium and carbon fiber (with a handle inlaid with teak) and cost over $1000.