15% drop FORMULA for tire pressure as a function of width and load
 

Hey all, you are probably familiar with the 15% Tire Drop chart, and maybe even the original article it was based on. While I greatly appreciate the sensible approach to optimal tire inflation those provide, I have always found it annoying that the chart maxes out at 700Cx37mm. How am I to figure out the optimal tire pressure for my 29x1.95 Vee Rubber V12 fatties?

So I crunched a little numbers, worked a little mathemagic, turned a little crank with Excel solver, and came up with a formula that fairly-well fits the set of lines in the 15% Tire Drop Chart. Here it is.

Let W be the tire width in mm, and let L be single-wheel load, in pounds. The tire pressure P (in psi) to achieve approximately 15% drop is:


So this formula fits most of the chart fairly well, to within about 2psi. For instance, for a 150lb load on a 32mm tire, the formula would give


which is pretty much bang-on what the chart shows. For my V12 (which actually measure out to about 46mm, even though they are labeled as 1.95"=50mm), my estimated front/rear loads of 100/150 would call for front/rear pressures of 38/52 (which I would round to 40/50 and tweak from there)

Note: the exception is that the 20mm line is NOT as well fit (the formula works out to be 10-15psi too high for 20mm, so there must be some physical factor coming into play as tire widths get extremely narrow that my formula is not capturing. Caveat emptor.)

Note: Yes, the numbers are suspiciously (pleasingly?) round! The actual numbers I got from solver using the load/pressure points I eyeballed from the graph, and using kg instead of pounds, were 1319.574, 0.745703, -25.3899, which yielded a total of 23.03 as a least-squares deviation for the low/high fit points from the 23-37mm lines. Rounding to 1320, 0.75, -25 bumped the least-squares total to only 25.96. And then the conversion to pounds 1320/2.2-->600 was rather serendipitous as well.

Note: This whole deal is designed for road riding only. For mountain bikes, refer to the original article, which provides a separate chart of minimum pressures, because the 15% drop rule is for rolling resistance, while a mountain bike is more concerned with traction, cornering, and suspension.

TL;DR

Seriously, am I the only one that thinks this chart is wrong? Can't people make their own decisions?

Only one or not, I don't understand your objection.

I look up recommended torque values when tightening bolts on my bikes (most of the time). I look at recommended tire pressures embossed on my car and bike tires. Why shouldn't I look at a table or a graph?

Of course they can and should make their own decisions, but having some information on which to make those judgements always helps.

Charts like this are only guide lines, as are the various rules of thumb for seat height, stem length, etc.

Despite the shortcomings (I find the values to be low for wider tires) the article and chart do show that wider tires at somewhat lower pressures can have lower rolling resistance than very narrow tires at very high pressures. It also shows the relationship between pressure, width and axle load. All in all it serves a valuable purpose -- as a starting point, but like anything else, shouldn't be taken as gospel.

+1. This is why I demonstrated how rounding and approximation were used in my process.

Funny, I find it to come in high. Compared to the calculated suggestion of 38/52 I found 35/40 to be very good for my commute. In particular, there is a triangular steel bar that I have to roll over (it is the track for a mechanical gate at my work), and 35/40 it absorbs the impact very well without bottoming out. Even 30/35 does not bottom out, but it feels like it is getting close.

It might be that there's a curve, and riders of different weights have different results. It also depends on pavement, and/or rider goals. On smoother pavements the drawbacks of higher rebound aren't there, so higher pressures make sense. On lousy pavements rebound and comfort become more important so one may drop pressure a bit.

Being fairly lazy, I pump my commuter's 2" tires to 60/50 at the start of the week, and let them bleed down about 10psi before pumping fresh. There's a short steep climb with lousy pavement on my daily ride. Early in the week the chatter and power loss on the bumps is pronounced, and I steer around them as much as possible. OTOH, on better pavements the lower pressure at the end of the week makes the bike noticeably slower.

All in all I find the higher pressures preferable, but not enough to pump more often.

Like so many other things, it's about trade offs and compromise.

Most people (especially those in a rush to argue with the article's premise) skim over this part:

So it's acknowledged for all to see that they wanted to determine "happy medium" tire pressures based on bike load and tire width, that folks could use as a starting point. :)

Maybe I underestimate my loaded weight but, on a recent trip, when I inflated my Grand Bois 584x32 tires to the chart, they looked like I was riding on flat tires -sure seemed like more than 15% drop. What should have been ~50/60 was inflated more like 65/70 on my trip. Incidently they held air very well and didn't need more pressure for the entire week.

(stop trying to estimate my weight)

i dont see any evidence given to support the
15 percent is optimal
claim

the fact it is a round number suggests that
it was chosen arbitrarily

and while there is a caveat that
rough rides need more and smooth rides need less
the idea that one magic amount of drop
is best for all tires
is a bit hard to swallow

however
it probably gets people closer to the mythical
optimum pressure
than guessing and squeezing the tire with the thumb

also
when i find my tire sizes and approximate wheel loads on the chart
it is pretty close to the pressures i like to run at
based on experimentation and personal preference

to the op
good job on the forumla

try to also
derive a formula
where nominal tire diameter
and desired drop
are entered

that would cover the weakness i see in your forumla as written
there is no compensation for wheel diameter
which should change everything as the length to width ratio
of the contact patch changes
and
it only works for 15 percent drop

Thanks. I have no resources to attempt to come up with a formula for other than 15% drop, or 700C. My formula is merely an empirical fit to the provided chart -- which is in turn an empirical graph of load/mm/psi combinations that experienced 15% drop as measured by a dial gauge. Neither of those approaches involves any kind of modeling of the physical forces involved, so there is no way with the data I have to do anything different.

Now the original article noted that his measurements included other amounts of tire drop than 15%, he just gave us the lines that passed through the 15% points. If Frank Berto is still around and has all of his extra data (measured drop for "50 different tires at 7 pressures (40 to 160 psi) and 8 loads (20 to 220 lbs)"), then it would be possible to develop a more general fit that also varies drop. But still that would be 700C only. Beyond that, somebody would have to conduct a fresh experiment using additional diameters.

Another sire. https://docs.google.com/spreadsheet/...hl=en_US#gid=0

But some people seem to think they need to follow it to the tee.

Per Jan and Frank, the wheel size is not very relevant, just the tire width. And as a reminder that neither article says "Thou shalt inflate thy tires to 15% drop":

tl;dr mainly because 15% tire drop on 23 and 25 mm road tires doesn't work for me. Too squishy, especially in the front when standing. Also prone to pinch flatting.

I also wonder where the 15% drop assumption comes from. Still, I like the article and the chart and have been using it as a guideline since I read it a couple of years ago. Good job on the formula, RubeRad. I appreciate it. davidad, thank you for the spreadsheet.

As a result of this article, I inflate my tires softer than I used to. No pinch flats yet. It was scary at first, but I'm getting used to it. And I'm thinking of switching from 32mm to 37mm on my commuter bike.

My wife has very wide tires, and she weighs less than 120 lbs. I'm scared to give her the optimal pressure. It just sounds crazy. I need to get over that.

OK, that's the second time. What's a "tl;dr"?

I would put down a dowel or a stick and have her ride over it and watch the tires deform. That would probably put your mind at ease.

Ooh, clever!

Your weight is fine, it's your 90lb bike I'm concerned about! :thumb:

Too long; didn't read. ;)

Ah, you learn something every day!

The chart is absolutely wrong. It has no accounting for the vast difference in tread and sidewall stiffness between various tires. Compare for instance the Conti Gator Hardshell to the Conti Supersonic. One of them will damn near hold you up without any air in it.

One of the best pieces of advice about product design and manufacturing I ever got, was some 40 years ago, bt it applies here.

"Never sacrifice good, on the altar of perfection".

This article and the related charts are a good starting place, but are not intended to replace experience based fine tuning. There are any number of variables that aren't included, including wall stiffness, wall shape (tire width/rim width) tread compound, and rider speed. If we hold out for some perfect scientific formula, we'll have nothing we can use as a starting place now. To their credit the authors were among the first to open a discussion of pressure, weight and cross section, so while it's not perfect, the information makes a good starting place for thinking about tire performance.

For example, rebound and traction loss are related to speed, and a pressure that seems to offer low rolling resistance and good traction at low to medium speed, may cause excessively skittish handling and loss of cornering traction on high speed descents.

Years ago we didn't use science or formulas, but were attuned to the issues and trade offs and found things like optimal tire pressure through experience. I as taught to increase pressure 5psi at a time, and riding under various conditions, until handling suffered, then dropping back to where it was OK. I still use a similar method, and as I described earlier seek balance between good ability to climb on bad pavement, and low rolling resistance.

Even after years of riding the same equipment, I'll still make an adjustment based on anticipated conditions.

I recently heard a variation of that sentiment: "At some point, you gotta shoot the engineers and just ship it!"