Road Fan

@Carbonfiberboy,
Again, thank you!

Can we go back? You asked if I see what you did. I see SOMETHING of what you did, but I don't fully understand it. Can you provide more explanation?
Does the constant 3000 work for everyone, or at least does it work for anyone else who's tried to use it? I am concerned about that because my team is a lot heavier than you are.

conspiratemus1

Carbonfibreboy's formula is based on LaPlace's law, which pops up whenever pressure vessels (the heart, arteries, steam boilers, and tires) are analyzed.

For cylinders, T = p * r / t,

where T is tension developed in the wall of the cylinder, p is the indicated gauge pressure, r is the radius of the cylinder, and t is the thickness of the cylinder wall. This "thin-walled" case holds when the radius of the cylinder is at least 10 times the thickness of the wall, so for most tires (and large arteries) we're OK. A moment of algebra will show that for constant wall thickness and a maximum safe design tension, the product of pressure and radius is a constant, the "3000" used in Carbonfibreboy's rule of thumb. It's messier in real life because on a wheel, the pressure vessel consists of the tire carcass, the rim, and the rim-tire interface where the two beads mate. Also, wider tires might (I don't know, never measured) be thicker than narrow ones; so to be more accurate you should include the tension-lowering effect of thicker sidewalls, which would allow a wider tire, if thicker, to hold a pressure higher than the rule-of-thumb value might suggest and still remain at a safe tension. But because over-inflating a tire blows the bead off the trim -- it doesn't split the tire carcass -- it is probably prudent not to view thickness as a safeguard against failure from over-inflation, especially since to my casual "thumb-and-middle-finger" testing, most bike tires are about the same thickness anyway. In other words, Carbonfibreboy's omission of tire thickness in his rule of thumb is not a fault but rather a feature.


So a rule of thumb that says divide 3000 by the tire diameter to get the max. safe inflation pressure seems a sensible place to start and is supported by physics. It's the same principle that shipbuilders use to figure out how thick the steam boiler in a nuclear submarine has to be. (The magic number for a steel boiler is of course many many thousands: hundreds of psi * several feet of radius.) The caution for us is that the weakest point is the bead interface. Some tires, regardless of safe inflation pressure, are difficult to get to seat reliably on some rims -- we've all been there. I think most of us, sensibly, would avoid those combinations, and not underinflate such a tire merely to keep it on the rim.


Joining the trend to wider tires, we've been experimenting with lowering the pressure to below the sidewall max, since they seem to be immune from pinch flats. In the past we used 25 mm tires inflated to 120 psi "because that's what tandemists do." We currently use 30 mm, the biggest that will fit, inflated to just 80 and Ms. C. loves the ride on our chip-seal. We're no slower, either, just as Jan Heine would have predicted all along. Our magic number might now be just 2400. (Crew + vehicle weight ~325 lb also. Friends of ours who are much taller and heavier (and faster) have profited greatly by modifying their bike to take 43 mm tires.)

Carbonfiberboy 

I'm not a nuclear reactor vessel designer, just an observant person. Over many years and many tandem tire models, from 23mm to 31mm, I noticed that good performance from each of these tire models did seem to adhere to a formula. Nice to see that the laws of physics apply in the real world.

We do a lot of fast, somewhat technical descending, so I'm not going to cut my pressure until I start pinch flatting on a pothole at 40 or so. Of course at our weight, I'm nowhere near sidewall pressure, so that's an easy decision.

That said, I have not purchased wide tires with sidewall pressures which do not fit into my formula, guessing that they have weak casings to save weight. And besides, I'm a bit addicted to the tandem aero advantage, even use CxRay spokes.

Road Fan

Thanks Conspiratamus1! That reminds me of some forgotten mechanics! So I made a table of widths and pressures for the 3000 safety criterion:

d [mm] pressure [psi]
21 143
23 130
25 120
27 111
28 107
30 100
32 94
35 86
38 79
42 71
48 62

So these are all the upper limits for which the beads should remain seated, since that is stated to be the main failure mode for a bike tire. This criterion has no correlation to the Berto chart, which deals with constant percentage tire sag. From my Berto calculation (post 1 this thread) each of my tires has to support 200#, and I assumed a target of 15% tire sag. What is good about this is that it gives decent rim protection. But Berto's pressure value (with my extrapolation of the chart along the x-axis) for this condition is that the 28c needs 146 psi, and the 32c needs 116 psi. Both of these wildly exceed the "3000" criterion. I notice CarbonFiberBoy's examples represent a tolerance of +/- 10 or 15%, and he's still with us and kicking. If I went to 32 mm tires (and the frame clearances are good!), that is probably about as good as I can get, in terms of tire criteria.

Question: in the "3000" formula, does tire loading truly have nothing to do with bead seating and its retention? It seems odd but correct, that the only effect of loading is to distort the tire at the contact patch so that the area of the contact path and the tire pressure apply force to the ground that is equal to the load the tire is supporting (bike + rider + gear, including the wheel itself). But still seems weird that Clydes (I'm a borderline Clyde) don't need wider tires than non-Clydes (sub-Clydes?).

OneIsAllYouNeed

A word of caution on the 3000psi*mm criteria. In my experience with a handful *hookless* tubeless rims and tires, they blow off around 2600psi*mm.
Tubeless-ready tires tend to have a stiffer bead than non-tubeless ready tires. Similarly, folding beads are stiffer than steel beads. Stiffer tire beads better resist tire blowoff.

Limited by clearance to a 700c x 32mm, your best specific tire options are likely the Continental GP4000S II 28mm (actually 31mm), rated to 115psi; Continental Gatorskin or Gator Hardshell, or 4 Season, rated to 102psi; or the Schwalbe Energizer Plus or Panaracer Ribmo 32mm, rated to 100psi.

conspiratemus1

Bead blow-off is the main failure mode from over-inflation. Pinch-flatting and collapse during cornering are important failure modes for under-inflation.I would not want to inflate any commonly available tire to the levels predicted by Berto's chart when extrapolated even to our modest weight of 325 lb. And we don't. I think what Berto would have you do is raise the pressure until tire drop is <= 15%, hoping that this pressure will not blow off the tire. (Likely it won't: I'm told that max. pressure embossed on the sidewall is half the pressure it takes to blow the tire off a sample of rims.) But I would still interpret Berto as showing that heavy riders should use wider tires, if for no other reason than to avoid exceeding max. pressure by such a wide margin. Remember that the "3000" number is just a way to convert a pressure*diameter relationship that Carbonfibreboy knows already works with one tire to a tire with a different diameter. It's not a gold standard that applies to all riders. But it is well-founded in LaPlace's law: a 25 mm tire at 120 psi develops the same tension as a 40 mm tire at 75. Whether this tension is the "right" tension depends on the weight of the riders and the integrity of the bead interface.

Road Fan

From Berto's original article it was clear he expects you to choose tires of a suitable cross-section to achieve the 15% criterion with your actual wheel loading. This of course implies wider tires for heavier riders. I may have confused you when I observed that loading (heavy rider) does not seem to be comprehended by the LaPlace equation. To accomplish that with a heavy tandem, at least in my case with 400+ lb, seems possible only with wide tires. There actually isn't a lot of difference between the two criteria, if you are going to stay within sidewall limits. I totally agree with your text that I highlighted.

I have no argument with the math of the LaPlace rule.

conspiratemus1

Just remember that a tire bears the externally applied weight by means of the circumferential tension developed in the carcass by the air pressure held within, quantified by LaPlace's law. So loading is inherent in LaPlace. The greater the weight, the greater must be the tension in the cords, else the tire will deform too much under load. You can raise the tension to a level that resists tire collapse by raising the pressure or increasing the diameter....but only as far as the tire/rim system can tolerate that tension. Note that making the tire thicker is another approach. A thicker tire develops less tension (which is force per unit cross-sectional area of the wall) for a given pressure and diameter (T=p*r/t) and would deform less under load, allowing a lower inflation pressure. This might be where Berto's graph fails: he looked at deformation under load of a whole bunch of tires of any given size and averaged each size. You might, instead, be interested in the individual deformations of several 32 mm tires in order to choose the one that deformed 15% with the lowest pressure. Downside is that thick tires absorb more energy in inelastic flexing and so roll with more resistance. No free lunch. In bicycles, birds, and airplanes, lightness removes so many constraints from design.

A practical suggestion would be to install the largest tires that will fit and inflate them to the max. sidewall pressure. Then ride over railway tracks at speed, the rougher the better (get stoker buy-in first!). If you don't pinch-flat you're golden. There is no need to try narrower tires because they won't roll any faster on long rides and will be less comfortable especially for stoker. I don't recommend this test on rough gravel because if you flat you're more likely to go down. If you do pinch-flat, inflate 10-15 % over the max. -- should be safe, really -- and try again. If you still pinch-flat, you should avoid riding over the things that cause pinch-flats. Avoid pot-holes and random rocks of course. Gravel roads might not be in your performance envelope. We knew a couple who walked over every railway track. You could modify your frame to take even bigger tires, as our friends did. Or find a thicker tire, but performance will suffer.

reburns

Here’s my empirical approach: get the biggest tires that will fit and that meet your criteria for rolling resistance, puncture and cut resistance, ride quality, etc. Start out with the tires inflated to the max pressure printed on the sidewalls. Experiment with reducing the pressure incrementally until you notice adverse effects on handling or you get a pinch flat.

I notice "squirminess" in handling when the pressure drops below our nominal values before we suffer any undue pinch flats. We put about 150/200 lbs load on the front/rear tires. I’ve chosen 28 mm (actually 32) Continental GP 4000 S2 for the front and 32 mm (actually 34) Continental 4 season for the rear. For our particular team, technique, equipment and conditions, 80/90 psi f/r results in a fast, smooth ride with flats few and far between.

Road Fan

That makes me feel better, too. And I see that your formula is about scaling any given pressure requirement, where Berto's work had a different purpose, more like a scalable de-rating rule.

Road Fan

With my wife in the stoker position and my now 66 yo body in the Cap's Chair, I am reluctant to use pinch-flatting as a diagnostic method. I hope this is understandable. It's like, "Oooo the spokes all broke! I musta done somethin' wrong! Owww, that really hurts!"

reburns

I am in exactly the same situation and understand completely. My point is that, at least in my case, handling issues show up well before any risk of pinch flatting. I’ve actually never experienced a flat on the road tandem due to tire pressure being too low.

Carbonfiberboy 

Well, there's that. In my tire experiments, we've usually pinch-flatted at low speeds trying to ease over something, like a curb-cut with a 2" lip at the bottom, or slowly crossing bad tracks. IIRC, we've never had one at speed, probably because I slow way down for stuff that doesn't look good. And at speed, hitting a normal unseen pothole, the wheel doesn't have time to drop into the hole far enough to cause damage. At lower speeds of course they'd be easy to see and avoid. I don't believe the whole tandeming thing is as fraught with danger as it might seem. Unless you're like a guy I knew who had a habit of taking corners way too fast and taking the machine into the shrubbery until his stoker refused to ride with him anymore. Doesn't seem to me that you're in that category at all.

"Tire experiments" as such were not intentional. You take your best guess and see how it goes. One learns something on every ride to start with.

Road Fan

Thanks and I appreciate the confirmation! Several times in this thread I've seen comments that amount to, "well, if you pinch-flat it's too soft" and I wanted to put a stake in the ground, that that's a poor way to set tire pressure - I'd also like to have adequate rim protection as I ride just for example. Which is kinda where I started the thread.

Carbonfiberboy 

I might say that pinch flatting or tire pressure has nothing to do with rim damage. You can get rim damage by getting a sudden sidewall cut, so you have zero pressure, and then successfully bringing the thing to a stop. I've had that happen. Pretty good chance you'll have to sand some dings out of the rim edge. That's really what one worries about, better have the moves hard-wired in your head. Another good way to pinch flat is to get a slow leak in the rear that you don't notice, then hit some little thing and pinch flat. I've had that happen. Almost unavoidable if you ride enough. I've never seen rim damage from a pinch flat, other than as I think I mentioned, when a single rider hit a 4" asphalt lip head-on. That'll do it. Nothing to do with tire pressure.

The issue with going wide is that conpiratemus is correct and the larger the tire, the lower must be the pressure or you blow off the rim or destroy a worn brake track. The pressure you can put on the rim is fixed. As you noticed, the Berto chart is pretty much guaranteed to put you into a very serious situation at the most inopportune time, like braking for a right hand hairpin..All you can really do is buy a tire your experienced tandem friends recommend and inflate it to sidewall pressure. Beyond that, one really can't go. We run 31 mm tires at 95, which is definitely more than they need, but I prefer it.

The use of my little formula is that one can start from, as has been mentioned, a 31mm Conti with a max pressure of 116, which gives you 3596. then divide the width of another candidate tire into that figure and see if you get a number less than its sidewall pressure. They're not all equal. Interestingly, it doesn't seem like tire thickness has that much to do with printed sidewall pressure. Contis are quite thin. Marathon plus in 28mm have a sidewall pressure of 110 for example.

That said, you may not need that much pressure but you probably won't experiment with less by the sound of it. Many stokers can tell rear tire pressure within 5 lbs by the feel of it.

That 31mm is on a 23mm outside rim. 23-24 mm rims are nice. I much prefer the feel of a tire on those wider rims.

Road Fan

The sharpness and height of a bump and the impact speed of any encounter with a bump are random variables. Each variable has a most-common value, and all the other possible values are greater or less than that value. So the likelihood of a bump being intense or light is one probability.

I’m not concerned about expecting tandem tires/rims or those of any bike to survive the worst case bump event, whatever that is. I also don’t expect a rim/tire to always last 10 years without some care or without wearout. The likelihood of various levels of damage is related to tire pressure, tire design, rim design, wheel design, bike weight, suspension/flex, and possibly rider technique (unweighting or bunny-hopping).

So the probability of rim or tire damage that would irritate me is the product of the bump severity likelihood, the level of damage likelihood, and my threshold for irritation. We could perhaps call that a satisfaction function, a mathematical model that is intended to represent bike rider satisfaction.

I don’t have any of the details of the most common values of any of the random variables or anything to share regarding my irritability, at least no scaling methods that would be relevant in a math model. But I think this shows that in my opinion, dissatisfaction due to both rim denting and tire flatting is more severe with more intense bumps.

We also know that if air pressure is zero the rim may be dented by even small bumps. The tire and tube can also be damaged by puncture or flatting. If the tire is fully inflated the rim is protected from all but the most severe denting and is more susceptible to blowoff in case of undetected rim damage.

I hope this illustrates why I see the effects on rims and on tires as two sides of the same coin, and to depend on some of the same causes.

Carbonfiberboy 

Rims are really pretty tough. A bit of your discussion is the reason I always carry a spare tire. My standard flat fix method is to remove the flatted tire and tube, replace both with new, don't even look for what caused the flat. Very quick and effective. The times I've run a little ways on the rim, some sandpaper back home smoothed up the edge, which was never rough enough to prevent a new tire mounting. Not to say you couldn't have a bigger disaster, but that's what friends are for. We've never gone down from a tire issue. There was a fellow used to post on here who was descending whatever big pass on the Furnace Creek 508 in the dark when one of his sidewalls went out. Probably doing 30-40. Stopped it upright, repaired and continued.

You're right, no math models, all one can go on is anecdotes, which includes personal observation. Here in the PNW, riding all winter, my rims last 2 years, so I replace one every year and alternate. Bummer, because my favorite rims are no longer available. But not that big a bummer because I had the opportunity to stockpile 3 of them.

We unweight fine, but have never developed the technique of tandem bunny-hopping, although some teams on here have. I call STAND or UP for anything that looks not so good. To stand and pedal, I call 1, 2, 3 on the right downstroke. We often do that to get through a bit of roughness or for tracks.

Main thing is to have fun and remember, if there's no blood, it doesn't count.

Road Fan

Thanks! I'm also not too worried about rim cosmetic damage - it's denting and out of round/true that bugs me. I seem to end up needing the brake shoes rather close to the rim, and a little lateral run-out can rub. As far as tandemer's technique, I think I mentioned I'm building my first tandem - I took the opportunity when a biking bud had to sell the real good steel frame he was holding in abeyance. In any case, Mrs. Road Fan and I will need to work on just starting and stopping. Luckily neither of us use clip-ons, so falling over is not the most likely problem! When we're 75 or so we might be at the bunny-hopping stage!

Reminds me, I need to order a good cushy stoker seatpost - the rear cockpit is going to be a little tighter than she's used to. Mrs. Road Fan is taller than the women my biking bud rode with.

It doesn't count if there's no blood AND if the shapes of all your limbs are normal, AND if you can move mostly normally!

Carbonfiberboy 

Our first tandem ride, we made it 20' before we fell over in our front yard. Better would have been: new captain rides with experienced stoker, around the block a few times or in parking lot or whatever. New stoker rides with experienced captain, etc. We once fell over on a loaded tour right in front of a church in the Czech Republic, just as the parishioners came out the door. That was pretty funny. Doesn't take much to screw up. We both ride clipped in, Stoker stays clipped at stops. She can rip out of 'em very quickly. On a motorcycle tour with gear and pillion, I once fell over at a French toll booth. That was embarrassing.

Road Fan

Yeah, not all falls are catastrophic, but we're only getting older, farther from the ages when kids bounce if they fall.

When I first got my Suzuki GT550, a pretty large and massive 550 cc two-stroke triple, it fell over a few times. In my 20s (around 1976), I rolled out of the fall and avoided being pinned. It was also low speed, so besides laughter, the biggest problem was to lift the bike back up. But using my legs instead of my back did the trick.