In praise of riding low pressure tyres fast

[JimK]

I don't mean to belabor this endlessly, but I feel like I am getting close to understanding the relationship between pressure and tire width... yet there is still something off, and I am hoping that by showing my thinking explicitly, maybe somebody will find my error.

Seems to me that the contact patch area can be estimated quite closely. If we apply enough load to compress the tire by x, then the contact patch area should be 2*pi*x*sqrt(r*R),
where r is the radius of the tire and R is the radius of the wheel:



Suppose we have a wheel of radius 13 inches and a tire of radius 1 inch. Suppose we load the wheel so the tire compresses by 15% of the 2 inch tire width, i.e. 0.3 inches. Then the contact patch area should be  2*pi*0.3*sqrt(1*13) = 6.8 square inches.

Whew, that can't be right! That would carry about 100 pounds at 15 psi.

[JimK]

FWIW, if you look at the Encyclopedia Britannica article that Dan so kindly posted, the contact patch area formula that I posted is exactly what appears there. Even more strangely, at the end of the article there is a table of tire sizes, pressures, and loads. Looking at the first column, a 28 inch wheel with a 2.5 inch tire and .19 inches of deflection, I compute a 5 square inch contact area. The table shows 70 psi carrying 360 pounds, so that is very much in line with 5 square inches.

That size is not far off a bicycle tire. To carry a 100 pound load, that would put the pressure down to 20 psi. But that is only .19 inches of deflection... the usual 15% Berto rule would call for .38 inches..  or 10 psi.

Maybe my problem is just the 15% rule. If that's really 15% of the tire radius, rather than of the diameter, that would pretty much put things in order. It seems I am off by a bit more that 2x, but still, that gets me in the ballpark.

[Danneaux]

Jim,

If I understand the 15% rule of thumb correctly, then it is a 15% drop in the rim height measured at the bottom, under load (compared to unloaded, however that is defined).  That would indicate radius rather than diameter.  Though it a terribly difficult to measure empirically.

The idea in measuring the rim at the bottom (or the axle centerline) is it provides a true measurement of casing tension reduction under load.

As for the actual amount of pressure in a tire...did you see those photos on the Schwalbe websites?  Their photo of underinflation looked noticeably flat to me!  The photos showing a properly inflated tire could encompass a pretty broad range of pressures: http://www.schwalbetires.com/tech_info/inflation_pressure

It is also interesting to read this...

http://performancesimulations.com/fact-or-fiction-tires-1.htm

...a third-party presentation and discussion of  Avon tires' research showing contact patch pressure not only does not remain close to constant under increased load, it never even approaches that of the air pressure in the tire.  Relevant to the foregoing, the author states,

Contact patch pressure is constant and equal to air pressure?  No, not even close.

Wide tires have a greater contact area?  From this data it appears very likely.  Which would mean the "wide tires are softer and therefore give more grip" argument is bunk.  The contact patch is bigger, and the contact patch pressure is lower.  Avon has several sets of tire data available.  Feel free to do your own analysis on any of the other tires.  It appears likely from looking at this data is that if lateral sidewall deflection were included, the contact patch size might change by a rather small amount when the load is doubled in a typical operating range.  The contact patch certainly does NOT get twice as long and the contact patch size certainly doesn't double.  The above tables show the absolute limit to how much the length and areas could increase.  In reality the changes must be even less.

Wow.  Again, he's talking contact *pressure* and not *area*.  This data and observations seem to apply most directly to Formula 3000 car racing tires, which are of vastly different construction than bicycle tires, though the basic ideas still have relevance.

I fear we may be the only two nutters still in this game, Jim.

Best,

Dan.

[Andre Jute]

I'm reading this with fascination but not contributing anything because I must still set up networks, and then catch up on a couple of lost weeks... Thanks for the break, fellows.

[JimK]

Our teenager lifts weights in the basement, so it was easy for me to acquire 100 pounds of iron. I parked my Nomad next to a bookcase and marked the position of the rack top against the bookcase as I loaded the rack with the 100 pounds. The whole thing was a bit sloppy, but my best measurement is that the rack moved down about a quarter inch. This is with about 50 psi in the tire. Grrr. There is a factor of 3 loose here someplace! The quarter inch is very much in line with the 15% rule and Schwalbe's recommended pressure. It's just way out of line with my theory.... and with the Encyclopedia Brittanica theory, for that matter.

Humbling!

[Danneaux]

Thanks, Andre!  With three of us in the game, we've got the critical mass to be scientists, not nutters.     Good luck on the network setup; looking forward to hearing from you when things ease up a bit.

Good thinking about loading the rack, Jim.  It is near-enough directly above the tire to get a pretty clear and accurate measurement.  'Sure beats my gymnastics.

Just for fun...if you have a stamp pad or water-soluble paint, it would sure be interesting to ink the tire tread and get some imprints on graph paper. 

Best,

Dan (who usually solves problems by calculation, formulae and inference, but *loves* rigging apparatus for empirical testing).

[JimK]

Still chewing! The section "How A Tire Supports Its Load" in

http://www.sheldonbrown.com/tires.html

really knocked me for a loop. Sure, the tire has to exert a force against the ground to support the load; that is just the contact patch, area times pressure. But the tire must also push up on the rim with that same force!

Obviously my first model is just way too simple. Let me try again.


On top there is a rim which contacts the tire at point B. On the bottom is a contact patch. The tire leaves the road at point A. I just show half the tire since the whole affair is symmetric.

Where the tire is not touching the ground, it will have a circular cross section. This circle will be tangent to the gound at point A.

What I calculate here is the cross-sectional length of the tire, which has two parts - along the contact patch, and then the circular part. The height of the rim off the ground and the contact patch width must cooperate to keep this cross-sectional length constant. I would like to solve this equation, expressing the contact patch width in terms of the rim height. That sure doesn't look feasible, though!

So I did the next best thing, which was the numerical approach. I just used dumb trial and error to find some patch widths and rim heights that would give the same tire length. For easy comparison, I present the drop in height, or compression, rather than the height. I plotted the contact patch width versus this compression, and also plotted my old formula. You can see that the new relationship gives much smaller patch widths. This is for a rim (half)width of 9.5 and a rim height at zero patch width of 50 - roughly my Marathon Supreme 2 inch tires on the Rigida Andra 30 rims.



This makes the contact patch areas about a third of my old calculation - which brings the pressures right in line with reality.

But it sure seems like this problem is overconstrained - I still haven't factored in the requirement that the tire support the rim with the required force! The more I dig into this, the more confused I get!

Truly humbling!

[Danneaux]

Jim,

You (like myself and others interested in the science of tires) may wish to take a look at a publication by the US' National Highway and Traffic Safety Administration and the Department of Transportation. ( http://www.google.com/url?sa=t&rct=j&q=pneumatic%20tire%20science&source=web&cd=3&ved=0CCsQFjAC&url=http%3A%2F%2Fwww.nhtsa.gov%2Fstaticfiles%2Fsafercar%2Fpdf%2FPneumaticTire_HS-810-561.pdf&ei=L9XiTrr_IIWNigL9_ODBBg&usg=AFQjCNFP7z68TbA8W2Df1q8J0hT1SREPjA&cad=rja ). It is an update to the previous reference standard in the field for automotive tire design, S.K. Clark's, _Mechanics of Pneumatic Tires_.  I especially enjoyed the sections on waves in rotating tires (and how their propagation is damped by hysteresis) and rolling resistance.  Though the application is specific to automotive tires, the maths for determining and analyzing the characteristics of casing and carcass design are largely applicable to bicycle tires.

The more I dig into this, the more confused I get!  Truly humbling!

Jim, you're in good company; the modeling of tire behavior and characteristics -- even those as relatively straightforward as rolling resistance and tire patch shape, area, and loading are not simple.  The authors of the above publication indicate (pg. 410)...

A tire is remarkably complex in its structure and geometry. A model embracing too many of the features becomes over-complicated and the basic understanding is lost.

For a real appreciation of the difficulties and complexities in modeling tire forces, see F. Koutny's treatise, _Geometry and Mechanics of Pneumatic Tires_, a Czech engineer from Zlin, original home to Tomas Bata, founder of a shoe-building firm that later produced the the Bata Biker cycling shoes popular in the late 1970s; one of the first truly mass-produced, walkable cycle-touring shoes with...rubber soles.  For fun, see the references... http://en.wikipedia.org/wiki/Zl%C3%ADn ...and... http://en.wikipedia.org/wiki/Bata_Shoes

Respect! for tire engineers, and Schwalbe have some good ones.  This stuff goes all the way back at least to 10 December 1845, when Scot Robert William Thompson ( http://en.wikipedia.org/wiki/Robert_William_Thomson ) was awarded a British patent for the first pneumatic tire (an air-filled tire for horse-drawn carriages).  This, some 40 or so years before John Boyd Dunlop's application for bicycles (the passage of time was responsible for Dunlop receiving a patent; the rediscovery of Thompson's previous patent was responsible for the revocation of Dunlop's).  This stuff is fascinating to me, and so are the people involved -- true founders and giants in their burgeoning fields.    

<whoo!> A deep breath and small diversion in the discussion of bicycle tire rolling resistance and tire science.

Best,

Dan.

[stormdog]

Hi

I have been following this subject, and was wondering if any conclusions have been reached on the pressures we should inflate our tyres to. I realize it will depend to a degree of weight carried.

I have a Thorn Raven Tour with Rigida Andra 30 Rims and Schwalbe Hurricane 26x2.00 tyres, I was wondering what pressures other people use depending whether commuting or touring, I do quiet a lot of camping touring so am sometimes heavily ladened but carry very little on my daily commute over the Welsh hills.

Thanks for your views

John

[Danneaux]

John!

A worthy call for practicality in application...

I'm running Andra 30 rims and Schwalbe Dureme 26 x 2.0 rigid tires that measure a true 47mm in section width.  I weigh 172lbs/78kg in riding kit and my Sherpa weighs 40lbs/18kg with a pump, fenders, lights, and empty bottles.  I have been really happy recently running pressures of 45psi/3.1bar in each tire, front and rear.  With the bike loaded to the hilt (109-154lbs/49kg-70kg with full water tanks and a week's food), I seem to be doing alright with pressures pushing toward 55psi/3.8bar or so F/R.

I'm still fine-tuning and fiddling myself, but that's what's working nicely at present for a comfortable, smooth-rolling ride at each end of the spectrum.  I have found pressure variations make little difference in the outward appearance of fatter tires, unlike narrow, higher-pressure road-bike tires.  Looking at the Schwalbe guidelines and photos, I think at my weight unloaded, I could easily and safely do day rides on the Duremes at the minimum 30psi/2.0bar without damaging the sidewalls.

Hope this helps,

Dan.

[JimK]

All my analysis is fun and I hope leads to some increased understanding, but I would still advise sticking rather closely to the Schwalbe recommendations:

http://www.schwalbetires.com/tech_info/inflation_pressure

I think you want to increase those numbers with load. The base figure seems to be about 90 kg total on both tires combined. If you are a heavier fellow or are carrying a big load, you'll want to notch the pressure up a bit. Schwalbe recommends 3 bar for a 90 kg load. If you have say 30 extra kg aboard, crank that up to 4 bar. The limit for a 19 mm rim like the Andra Rigida 30 is apparently 5 bar, so you won't want to carry more than 60 extra kg.

Of course all of this is rather more precise than is really meaningful! But it's a starting point and then you can experiment to see what works for you and the conditions you ride in.

[stormdog]

Thanks Dan and Jim,

I will now do some weighing to check my tyre loading, and start doing some testing

Will let you know my results.

May be a few days as the forecast is for very stormy weather this week, and my route to work and back is over some high exposed roads, so may be a little bit of a problem trying to compare like for like.

thanks for your help

John

[revelo]

Interesting discussion. I recently completed a 1000 mile tour of the Mojave desert area of the Southwest United States, about 70% dirt road, 30% paved roads. Initially, I ran Schwalbe Marathon Extreme 2.25 (57-559) at about 42 PSI (about 2.8 bar) for the rear and 40 PSI (about 2.7 bar) for the front. When I had problems with sand, I deflated to 30 PSI (about 2.0 bar) for both tires, which helped a lot. Later, when I returned to the paved road, I reinflated back to the original pressures, then deflated again when I hit sand, etc. This got old fast, so I finally decided to deflate to just 36 PSI (about 2.5 bar) and see how that worked on sand. And it seemed to work just as well as 30 PSI. Then I left the tires at 36 PSI when I returned to pavement and the tires appeared to run as fast as at higher pressure. So that is some field experience in favor of lower pressures.

This tour was on a MTB. I just ordered a Nomad MK2 and will have it fitted with Schwalbe Mondial 2.15 (55-559). I will probably run these at the same pressure as the Extremes, or maybe slightly higher, say 38 PSI (about 2.6 bar) for the rear and slightly lower for the front, say 34 PSI (about 2.4 bar). My weight is about 85 kg dressed and a typical load would include 6kg of camping gear, 4 kg of food and 12 or so liters of water, so the total load would be 107 kg above the bike weight (about 18kg I imagine). 125 kg - Schwalbe's 75kg = 50kg. Divide this load in half gives 25kg additional per tire above Schwalbe's base loading. 35 PSI recommend pressure for 55-559 * 1.25 = 44 PSI. This sounds right for someone traveling exclusively on paved roads. But for someone like me, who is mostly on dirt, with much of that dirt being sand, 35 PSI or so is probably better.

[Danneaux]

Hi Frank,

I've enjoyed looking at your blog and could see the Nomad coming; glad it will soon arrive.  Will you be using the same luggage setup on the Nomad?  Looks as if the MSR Dromedary would fit the frame triangle the same way as on the Novara Portal.  Same for the hiking staff.  The Thorn rear rack will transfer right over.

Also, on your new Nomad...have you decided to try front panniers and rack, or will you stay with your existing handlebar-bag setup?  With the water mid-frame, you're probably pretty well balanced F/R on weight, so you should be set with pretty equal tire pressures. <nods>  Yes, the Mondial 2.15s should give you a nice wide footprint on the soft stuff, especially at 30psi.  Please keep us updated as to how the tires do with this pressure under load.  I am especially interested in how the sidewalls fare, not only with this pressure, but with the Great Basin's prevalent goat-head puncturevine.  I intend to carry some Mr. Tuffy liners for use when I get to where the goatheads are worst, but will leave them out as I transit to and from Oregon and Claifornia through the Cascades.
 
'Shame we can't find dehydrated water in the outdoors stores.

Looking forward to pics when you get it all set up.

Best,

Dan.

[revelo]

I've enjoyed looking at your blog and could see the Nomad coming; glad it will soon arrive.  Will you be using the same luggage setup on the Nomad?  Looks as if the MSR Dromedary would fit the frame triangle the same way as on the Novara Portal.  Same for the hiking staff.  The Thorn rear rack will transfer right over.

Also, on your new Nomad...have you decided to try front panniers and rack, or will you stay with your existing handlebar-bag setup?  With the water mid-frame, you're probably pretty well balanced F/R on weight, so you should be set with pretty equal tire pressures. <nods>  Yes, the Mondial 2.15s should give you a nice wide footprint on the soft stuff, especially at 30psi.  Please keep us updated as to how the tires do with this pressure under load.  I am especially interested in how the sidewalls fare, not only with this pressure, but with the Great Basin's prevalent goat-head puncturevine.  I intend to carry some Mr. Tuffy liners for use when I get to where the goatheads are worst, but will leave them out as I transit to and from Oregon and Claifornia through the Cascades.
 
'Shame we can't find dehydrated water in the outdoors stores.

Looking forward to pics when you get it all set up.

I don't mean to hijack this thread, but I will address the above questions:

I'm not sure what version of my website (http://www.frankrevelo.com/hiking) you saw. I've been updating it and there is a now a trip report available (http://frankrevelo.com/hiking/trips_2011_11.htm). The hiking staff idea was an experiment and has been rejected. I encountered very few stray dogs, which was the main reason I wanted the staff in a quick-draw position for use as a weapon.

I do not want front panniers. My maximum water carrying capacity is 19 liters, but I never actually carried more than 16L, and about 6L of that I kept in the front triangle. That is sufficient weight to keep the front of the bike from rearing up too much, since my rear rack load is not that heavy. What I discovered is that a little rearing up is actually beneficial when traveling on sand. If the front is heavily loaded, then when you hit a patch of soft sand, the bike stops dead in its tracks. The only time I've had problems with the front rearing up was while testing my bike, unloaded, on steep and rugged uphills roads in the mountains around where I live (Reno, NV). But I can't pedal up these kinds of roads with the bike loaded, so that is a moot point. When I encounter this sort of road with a loaded bike, I just get off and push.

I am not a believer in tire liners, especially since Schwalbe tires already have a good protection belt. I think stans sealant in inner tubes is a much better idea for dealing with goathead. Read my report on flat prevention in goathead territory at http://frankrevelo.com/hiking/biking_flatprevention.htm

Now back to tire pressure. I'll definitely report my experiences with the Schwalbe Mondial 2.15. As I wrote before, I'll probably start with 36 PSI (2.5 bar) or maybe a little lower on the front and higher on the back, and then lower the pressure until I get something that works reasonably well on dirt roads. What I won't be doing is adjusting the pressure back to something higher when I go from dirt to pavement, since that is too much trouble. Also, lower pressure is safer if I need to jump off the pavement onto a soft road shoulder due to traffic coming up from behind. The more I think back on my recent trip, the less important going fast on pavement is, even assuming (and this is what this discussion is all about) that higher inflation makes for faster travel. What really matters to me is not bogging down in sand.