|   After the geeky braking debate now the whole deal! (long) | Cloxxki
Dec 24, 2003 12:20 PM | | Hi all,
I really enjoyed reading the brake debate for 26" vs. 29", and I'm sure the last thing hasn't been said about it yet.
How about we as the world's pioneers in 29"ing (new word?) work out all physical pro's and con's of 29" bikes over 26"? (you can still click away from this topic at this point, it's going to be real long and boring!)
I think it would be good to establish a short list of indisputable numbers that will tell you what REAL differences there are between 26" and 29".
As far as pure psysics are concerned, the following aspects should be covered :
-Realistic weight differences for complete bikes
-Rolling resistance (on glas, dirt, sand and mud)
-Effect of rolling resistance on terminal speed, as 200W, 300W and 400W (on glas, dirt, sand and mud)
-Climbing speed between the two, factoring weight and rolling resisance, do they even out? If so, at which speed?
-Braking (rim and disc, power and heat build-up)
-Acceleration (with and without rolling/air resistance in the math)
-Grip and Traction due to different shape of contact patch
-Comfort (peak load on rider's arms and behind)
-Behaviour on medium and large step-ups/drop-offs.
-Required tire pressure to have equal pinchflat resistance between both wheelsizes
-Any I forgot?
All this might even help predict laptimes (race finish time).
Something that's probably hard to put into numbers is handling. From what I observe on this forum and with people I speak to, we're still working towards ideal 29" geometries, letting go of the 26" wisedome values.
Okay, shall I set some base properties to calculate with?
26" vs. 29"
rim 440/480g
tube 180/200g
tire 510/560g
nipples (both sizes) 66g
spokes 360/410g
fork rigid 1000g/1035g
fork sussy 1500/1565g
rider+gear 80kg
bike (26") 11kg
Any conclusions from this debate will probably end up somewhere in a magazine article or 29" FAQ, so we better get it right!
I know, it's a lot to ask, but does someone have any points they'd like to give a go at?
I'll kick of with my take on complete bike weight.
-I suggest to make frame weight a draw, chainstays and downtubes evening out headtube.
-Although I love to go into details, I'll spare the world the effects on chainring sizes and chain lengths
-Note that in this calculation 26" and 29" share the same spokecount, which could mean weaker 29" wheels, although high-end parts seem to suffice for the most of us.
My go :
2x rim @ 40g =80g
2x tube @ 20g = 40g
2x tire @ 50g = 100g
Added weight at ~327mm radius from axles : 220g out of 2546g (26" is 2326g @296mm radius).
Spokes : 50g @ ~170mm radius from axles
Fork : 65g as most bikes are hardtails
Total scale difference : 335g that the 29" bike is heavier, all parts being of equal quality.
Of the complete weight, the 29" penalty is only good for
(335/(80000+11000)) * 100% = 0,368%
This 0,368% is effective on rolling resistance (always when touching the ground) and gavitational force (climbing/descending). For acceleration, formulae from the braking power tread can be borrowed. This time, as leg power is a couple of time smaller than braking force, weight should play a more significant role in the equasion. I can't do that math (just highschool), but you geeks can!
Challenge
To get an idea on how things turn out, let's build a hypothetical course.
Starting for 10s at 5m/s (during technical section), accelerating with 500W to speed that belongs to 300W, then holding speed with 300W of power for 40s. All over a soil that's the average of the asphalt, grass, dirt bumps and mud we encounter through a season.
How many meters has each bike travelled?
Does is make much defferent for the outcome if climbing is involved?
Effects of wheelsize on speed through corners and technical sections IMO is very significant, but probably not very easy to put into number and let the world believe.
Any suggestions on any I've assumpted so far before we gather data and facts?
Let's get is straight for once and for all, all the scientific pro's and con's.
Happy trails and holidays! (I'm going to combine both)
J |
| Dude, you're a Hella funny geek! | JAK
Dec 24, 2003 8:23 PM | | I gotta say I lost it all in my laughter from your drawing.
Keep on keepin' on! |
| Cloxxki you need to get laid so bad! (nm) | phatlizard
Dec 25, 2003 11:35 AM | | |
| The story of the pot and the kattle? | Cloxxki
Dec 25, 2003 3:13 PM | | Actually, I have no complaints on the inter-personal level, but thanks for your warm concerns :-)
What I really need right now is three 4-hour rides, 2 jogs, 3 swims and 2 spinning sessions a week. My bodyweight has been quite stable over the past months, but fat seems is eating away muscle, while it's supposed to be the other way around. No way I'm gonna be in shape in time to win that first race mid-March.
I díd do something active today, I built a bike! I'm SO out of shape, even that took me 5 hours...
A *cough* 26" bike out of 2nd hand, obsolete and cheaply acquired parts that the g/f will borrow as a beach- and training bike.
Tomorrow a SS CX race, and maybe if I don't feel exhausted enough after that, a *choke* 26" MTB race afterwards (starts at 12 and 14, same local event), which will hopefully mark the very last of it's kind in my carreer.
Everyone too much affected by the turkey to get this topic going on topic? Maybe I should try and post it again later on? |
| A few thoughts | FullSizeWheeler
Dec 26, 2003 2:25 AM | | I guess that somewhere some single individual with the whole picture needs to make a draft of the whole thing, before quality contributions and comments will come.
I also guess that such article or FAQ, like you hint, needs to be issued by some kind of formal group, like the magazine that you mention, MTBR, Gary Fisher Bicycles, or some frame builder, if it is to be viewed as trustable. "Testimonials from a collection of anonymous surfers" might not be so credible.
I sure would like to read a thorough article or FAQ on wheel size, with the scientific, neutral, and unbiased tone that we today can find in articles discussing frame size, but also a more "selling" version. The FAQ at the braking forum is one way to do it with a good outline, depth, and tone. |
| Easy... | Boj
Dec 27, 2003 2:37 AM | | For static cycling (forces in equilibrium - not still) this is how it goes:
P = F*V
P - power (W)
F - force opposing movement (N)
V - speed (m/s)
There are 4 things that watts from your legs go into when cycling:
- Rolling Resistance
- Air Resistance
- Drivetrain losses
- Gravity (applicable only if climbing a hill)
So complete equation for cycling on any terrain (or planet):
Cp*P = [m*g*sin(x)+m*g*Cr+0.5*p*V^2*S*Cd]*V
where:
m - mass of rider and bike (kg)
g - gravitational constant (9.8 m/s^2)
x - angle of the incline in degrees
Cr - coefficient of rolling resistance
p - air density (kg/m^3)
S - frontal area (m^2)
Cd - coefficient of drag
Cp - Coefficient to account for drivetrain losses
Anyway to go see whether 26" or 29" is better in a race we need to know which one minimizes better each of those 4 parameters overall so that there is least resistance to movement.
Rolling resistance is the most important one for ANY MTB. This is where most of the resistance for a MTB race comes from and this is a function of mass of the bike + rider (as well as tires + tire pressure and other less significant things). While I'm sure 29" wheels have lower rolling resistance there is no test data (as far as I know) showing how much. Also there is smaller choice of tires for 29" wheels so you can't get some super low RR tire (like Nokian NBX lite or Twister SS).
Air resistance is negligable in MTB most of the time. This is a function of frontal area (A) and coefficient of drag (Cd) or as just a single number Cd*A. 29" wheels would have greater Cd*A (Someone could investigate how much by on analyticcycling.com) but I doubt this would manifest itself much for a MTB race as there little air drag cause speeds off road are not large.
Drivetrain losses are a function of rider power output (Cp is usually given as 0.98 or thereabouts in cycling calculators) and this is a function of stiffness of the drivetrain amongst other things. Doubt that there is much difference here from 26" to 29".
Gravity when climbing a hill is purely a function of mass. Simple enough here.
So since Air drag + Drivetrain = Ignore, the question is how much rolling resistance do you save on a 29" bike to offset ~334 g increase in mass (which is a penalty for rolling resistance and when climbing).
In my (spare time) research I have done on this subject before, I'd say that even small saving in rolling resistance will be better than large savings in weight. If aim is to calculate how much faster you'd be on a 29" bike then we need to know how much rolling resistance you save for different sized wheels (all things being equal ie tires, tubes etc). Someone can do some searches on the net for some tests done on this (I have come across some papers on this in the past) and we can see if we can apply their results without much pain - I'd do it but I got to run now. Will post more later.
PS
In assessing what is faster I have ignored dynamic cycling (braking, accelerating, handling etc...) becaause I think there isn't that much of it in a typical MTB race for them to be significant. |
| Easy... | Cloxxki
Dec 27, 2003 6:56 AM | | Great write-up!
I agree with your PS, but the thing is, THAT's to be established as a fact before naysayers will as much as consider taking a 29" bike around the parking lot.
In today's group training (me out of shape, bike so-so), I've seen that my 29" hardtail corners better than any FS 26" bike ridden by very capable riders. Rail track - style grip levels, zero speedloss through typical messy 90º turns.
What would be interesting, is to build a 29" Supercal and a 26" Big Sur, both with Nanoraptor tires (Or Notos, or Mythos, etc), I'm quite sure those will be pretty comparable in quality.
Ideal test course would be a mild descend that requires neither braking or pedaling to complete. I already did such a small test, over roots and bumps, around 120m total. 29" won by over 1km/u (terminal speed into sharp corner) after both bikes started the course with 10km/u and finished around 24km/u. Me on my 26" racer couldn't compete with my buddy, first-time riding my Fisher, and we're both the same weight and of similar riding talent. Swapping bikes didn't change the result, again 1km/u for the Fisher.
Hard to really clock exact times there, but either 29" was 0,5 km/h avering the course, making for 1 km/u speed difference at the finish, or it's just 1 full km/h faster once speed has built up.
24km/h is a ery common avarage race speed for me, imagine how this would mean over a 60 min race where I'm 80% of the time not braking or in technical stuff. Close to a minute, in my calculations. That the difference between 15th and 10th for my racing!
Anyone know a place to test rolling resistance this way? No braking and no pedaling required, at typical flat XC speeds. Normal riding position (aerodynamics), picking the best lines possible naturally.
Any given difference between both standards could be compared with the theoretical difference in acceleration. Someone's heart rate monitor print-outs could sheds light in the acceleration that occurs through a race. How often to overcome how much speed difference? |
| Easy... | n8ofire
Dec 27, 2003 10:01 AM | | wow, that's great information.
I do have one comment. It seems to me that dynamic cycling is of utmost importance to this issue as one of the major arguments against 29"ers is that they are no good in the technical/twisty stuff (which requires a lot of on/off the brake.) Not many people argue that 29"ers are slower on the straights. Still, I would like to learn more about how much faster they are in the straights. Thanks again for your input. |
| tire contact patch and rolling resistance | dgdixon
Dec 27, 2003 10:28 AM | | The following is a description of study that Santana Cycles conducted to determine the advantages of 700c wheels vs. 26" wheels. While the study focused on tandems (and is several years old), it describes why the longer contact patch of a 700c wheel causes less tire deformation and lower rolling resistance. His conclusion is that the bigger wheel will be 2-4% faster due to decreased rolling resistance.
700c vs. 26": Testing Reveals Best Choice for You
by Bill McCready, President of Santana Cycles
"Santana sells similar numbers of tandems with both wheel sizes and has no ax to grind.
Four years ago a respected bike designer confidently predicted the impending demise of 700c tandems. While this was not particularly frightening to Santana (we had designed and promoted 26" road tandems as far back as 1983), it also didn't ring true. I've watched as hundreds of customers tested both sizes before making a decision --- was it possible the majority who chose 700c tandems were mistaken?
Many people who advocate one size over the other insist on comparing fat 26-inch tires and skinny 700c tires. Some make recommendations based on the availability of a particular tread pattern. Others confuse the issue by comparing 700c tandems designed for pavement with 26" tandems designed for dirt. Santana's question was simple: if you were to eliminate the differences in tread width, tread pattern, inflation pressure and frame geometry, is a 26" wheel superior to a 700c wheel strictly on the basis of its diameter? If yes, why? In an attempt to discover the truth, we prepared some test tandems and asked a number of teams to evaluate them.
To reduce extraneous perceptions our test bikes used identical tubing and direct-lateral frame style, 26" and 700c rims produced from the same extrusion, and tires with the same width and tread pattern inflated to the same pressure. The honest attempt was to discover the best size --- after all, life here at Santana would be a whole lot simpler if we could standardize on 26" wheels.
But first, some background. The argument over wheel size did not start with tandem riders. Alex Moulton of England produced pro racing bikes with 14-inch sew-up wheels in the late-'60s. In the mid-'70s, Tarn Cycles of Chicago built a series of Campy-equipped full-race singles (and at least one tandem) with 20-inch wheels. In the early-'80s California's first production mountain bikes, built by Victor Vincente, were equipped with 20" wheels. All of these builders argued that bikes with smaller wheels would be superior due to lower weight, stronger wheels, quicker acceleration, and less wind resistance.
Critics of these designs claimed bikes with smaller wheels were slower and less stable. While slower was difficult to prove, some organizers banned small-wheeled bikes from racing (where they might have disproved the "slower" argument) fearing "diminished gyroscopic effect" would inevitably lead to crashes in pack racing events.
Fred de Long, Technical Editor of Bicycling, disproved the "gyro" theory in the late '60s when he assembled a unique bike with side by side front wheels --- a normal front wheel plus an identical counter-rotating wheel slightly above and to one side. The second wheel (which rotated at the same speed but never touched the ground) offset the gyro effect of the first. His finding: a bicycle's gyro-stability is a myth. He postulated (and I agree) that all us cyclists remain upright by continually steering through/across the path of our imminent fall. (You can quickly prove this to yourself by riding a bike with an over-tightened headset --- the results are extremely convincing).
Three years ago there was yet another resurgence of interest in road-racing bikes with smaller-than-700c wheels. For a time you could buy road racing bikes with 26-inch wheels from many serious builders including Serotta and Paramount.
While a few large-frame time trial and triathlete bikes are still built around a pair of 26" wheels, the designers of these bikes are admittedly chasing tiny aerodynamic and weight advantages that will be lost on a tandem (where doubled power reduces the significance of these advantages by 50%).
So what did we learn during Santana's testing? Our panel of testers uniformly found 700c tandems were more stable at higher speeds. Most testers also believed the tandems with 700c wheels were faster. The difference in "feel" was substantial enough so that an envisioned follow-up "blind" test with carefully shielded-from-view wheels was deemed unnecessary.
Why were 700c tandems clearly more stable? At the time of the testing, none of us had a clue. I later developed a theory, first published three years ago, that the answer was due to the shape of the tires' contact patch (footprint). If the same mass is supported on tires inflated to the same pr essure, the area of the contact patch must also be the same --- this is, after all, the meaning of p.s.i. or "pounds per square inch." The difference in wheel diameter causes the footprint of the bigger wheel's tire to be more elongated than the footprint of the tire on the smaller wheel. I reasoned a longer footprint would provide greater directional stability at high speeds (as is the case with longer skis, surfboards, and skates). Until someone comes up with an alternative explanation, this theory not only explains the increase in high speed stability, it also explains why off-road riders might reasonably prefer 26-inch wheels --- the rounder footprint provides less steering resistance and easier maneuvering at low speeds.
While my original "footprint" theory explained stability, it didn't explain the perceived difference in speed. I originally thought it probable our testers were mistaken about a speed advantage for 700c wheels. If they actually rode faster with 700c wheels, I felt certain it was an ephemeral result of enhanced rider confidence. Put simply, if riders on 700c test tandems felt more confident at higher speeds (because of stability resulting from the shape of the footprint), this confidence might allow a temporary increase in performance. If there was an enduring speed difference, it seemed likely to me the lighter and smaller 26" wheels would have the advantage.
Some of you might think the difference in diameter between 26" and 700c is too small to matter. Actually, even though we all know 700c rim is slightly smaller than 27" rim, a 700c rim is a full 2-1/2 inches larger than 26" rim.
Two-and-one-half inches?! How can difference between 26" and 27" exceed 2-1/2"?! Answer: a ridiculous tradition dictates that sizes of bicycle wheels --- unlike car and motorcycle wheels --- indicate the nominal outside diameter of the TIRE, and not the actual diameter of the rim. While the out side diameter of a traditional 26-inch "balloon" tire is about an inch smaller than the original 27-inch "racing" tire, the rim is nearly 3 inches smaller. The same tradition exists in Europe where there are no fewer than 4 diameters of rims that accept "650" tires (labeled 650-A through 650-D). To compare the "real" size of a rim or tire you must know the "bead seat diameter." Fortunately, this number is found molded into the sidewall of most tires. The real size of a 27" rim is 630mm (about 24.8"), a 700c rim has a bead seat diameter of 622mm, and the "26-inch" rim found on tandems a nd mountain bikes is only 559mm (a mere 22"). If matching width tires are installed, the outside diameter of a 622 (700c) tire is 63mm (2.5") larger than the outside diameter of a 559 (26") tire.
I've since realized the testers who reported faster speeds on a tandem with 700c wheels were correct --- and here's why:
Remember that the area of a tire's contact patch (or footprint), because it is purely a function of weight and inflation, owes nothing to the diameter or width of a tire. It follows that our test tandems with 11% smaller wheels produced footprints that were exactly 11% shorter and, therefore exactly 11% wider. Shorter explains the stability difference and wider explains the speed difference.
Why is wider slower? To apply the extra width against the pavement, the tread and sidewall of the smaller yet equally-wide tire is forced to undergo a great deal of additional contortion --- and tread and sidewall squirm are the primary causes of rolling resistance.
Is the difference in rolling resistance enough to produce a significant difference in speed? Because rolling resistance is a much smaller factor than wind resistance, until a few months ago I would have guessed no. Today I'm convinced otherwise --- whereas aerodynamic and weight differences are probably only half as significant for tandems (because of doubled power), internal tire friction is probably twice as critical (because of doubled mass). Even if 26" someday proves itself the superior size for road racing singles (it hasn't yet), the optimal wheel size for a racing tandem will always be larger.
While determining an exact difference in rolling resistance would be fairly easy, the effect on speed is difficult to ascertain. My best current estimate is a 26" tandem with equivalent rims, tread width, tread pattern and inflation will be 2-4% slower than a 700c tandem. While this will be a small difference for those who want the flexibility of using their tandem off-road, those interested in ultra-fast pavement rides might expect a cruising speed difference of up to one mile per hour (or a century finishing time difference of 5-10 minutes).
A couple of final thoughts about ultra-fast road rides on a 26" tandem. To achieve the same gearing as a 700c road tandem with a 54 tooth chainring, a 26" racing tandem will need a 60 tooth ring --- which is incompatible with the curvature of modern front derailleurs. And when you want to stop, because braking power is a squared function of effective brake radius, a rim brake on a 26" tandem is 19% less effective than the same brake on a 700c tandem.
Does this mean 26" tandems are stupid? Hardly. If you want to conquer the toughest terrain, 700c wheels simply aren't strong enough. And if we built a 700c frame with sufficient clearance for as-yet nonexistent 2.5" knobbies (700x63), captains shorter than six feet would have a hard time straddling the top tube.
If you want a tandem for tackling rugged trails or rutted fire-roads, a 26" tandem with clearance for wide knobbies is the only choice. If you can limit your off-road excursions to graded dirt, a good 700c tandem is adequately strong and will always be faster on pavement. "
This text came from http://www.gtgtandems.com/tech/700-26.html |
| tire contact patch and rolling resistance | Cloxxki
Dec 27, 2003 1:45 PM | | "Fred de Long, Technical Editor of Bicycling, disproved the "gyro" theory in the late '60s when he assembled a unique bike with side by side front wheels --- a normal front wheel plus an identical counter-rotating wheel slightly above and to one side. The second wheel (which rotated at the same speed but never touched the ground) offset the gyro effect of the first. His finding: a bicycle's gyro-stability is a myth. He postulated (and I agree) that all us cyclists remain upright by continually steering through/across the path of our imminent fall. (You can quickly prove this to yourself by riding a bike with an over-tightened headset --- the results are extremely convincing)."
I have a set of ultralight carbon wheels, and when I put light road tires ont hem, the bike can handly be ridden without hands.
The counter turning second wheel may take away the effect you feel when you hold a turning wheel by the axle end and lift one side. I bet this doubel wheel setup is actually more stable than just one wheel, due to the added gyroscopic weight.
Back on rolling resistance? Who's got the course and who's got the pretty much identical 26-29" bikes? I'm sure we can find someone with 26" Mythos, Notos, Nano or Moto tires. |
| The skiing parallel (long) | FullSizeWheeler
Dec 27, 2003 1:18 PM | | I agree that we can never strictly by physics or mathematics ¡°prove¡± that bigger wheels are better, but that we need to know the governing physics to be able to answer the most common 26¡±-minded questions. I don¡¯t know what this may be worth, but it¡¯s a way I like to look at bike wheel size:
Choosing wheel size has a lot in common with choosing ski length. Wheels and skis are both the supporting contact between the ground and a person traveling at high speed along the ground.
SKIS
The main, determining factor in ski length selection is the skier¡¯s size. Sometimes, the selection models use skier weight, sometimes length, and sometimes both. In all models, a heavier or taller skier is calling for longer skis. The reason is intuitive. Longer skis spread out bigger mass over a bigger area, maintaining stability and support for bigger skiers. The ski selection models typically also have a clause saying that individual preferences and skiing style may call for slightly longer or shorter skis. Skiers who are skiing hard or fast are often recommended slightly longer skis than beginners and those prefering lower speeds.
Here¡¯s one typical example of alpine ski length recommendation:
Step 1: Choose ski length from this table:
< 54 kg: 155 cm
54-70 kg: 167 cm
63-71 kg: 174 cm
72-80 kg: 180 cm
81-90 kg: 187 cm
> 90 kg: 195 cm
Step 2: Using the table above as a starting point, consider these factors to decide whether you should stay at the recommended length or move a size longer or shorter:
Shorter: lighter, more maneuverable, easier to swing around (important if you use muscle power to rotate your turns), easier to carve on groomed slopes, easier to negotiate moguls, easier and safer when skiing through tight trees and other obstacles. Suited for: less experienced skiers, slower speeds, shorter turns, groomed, gentle runs, skiers who prefer wide skis
Longer: more speed, more stability, more flotation, less chatter, more control. Suited for: skilled/aggressive skiers, faster speeds, long, swooping turns, soft and variable snow, skiers who prefer narrow skis
BIKES
Now, let¡¯s look at bike tires, as compared to skis. At a bigger rider¡¯s mass, we would want a bigger contact area to spread the mass over, just like in the ski case. Otherwise, the pressure onto the ground would be bigger, which would give two disadvantages: The wheels would roll deeper, and therefore slower, in the ground, and the shear stress would be higher at turning, accelerating, and braking, which would lead to less control on most types of off-road terrain.
So let¡¯s now make a wheel size recommendation, with the ski case as a model:
Ideally, we should make an experiment involving twelve different bikes and eighteen persons: The bikes should have frame sizes S, M, L, and XL, and wheel sizes 24¡±, 26¡±, and 29¡±, with one wheel size per frame size. The persons should weigh 50, 60, 70, 80, 90, and 100 kg, and be beginners, intermediates, and pros, one at each weight. All the test persons would be asked to take a couple of days of serious rides in different terrain with all three bikes having their frame size. Finally, their comments would be summarized.
In the absence of a result from such a test, let¡¯s look at the typical recommendations for kids, youth, and teenagers bikes, and extrapolate them to adult weights. After all, those recommendations have developed over time, showing a basic relation between human weight and suitable bike wheel size (For the interested, here¡¯s an illustration of that thinking: FullSizeWheeler "What rider size are 29ers suitable for?" 9/19/03 1:56am). I have averaged recommendations for 12", 16", 20", and 24" wheeled bikes, and extrapolated them to 26" and 29". Finally, we look at the second step of the ski recommentations and transform them to biking terms.
Here¡¯s what we get, and the type of wheel size recommendation I would like to see:
CONCLUSION
Rider Weight, kg (lb) MTB Wheel Size
< 50 (110) 24¡±
50-59 (110-130) 26¡±
¡Ý 60 (131) 29¡±
You may go one step smaller if you prefer lower speeds, shorter turns, groomed, gentle runs, or wide tires
You may go one step bigger if you prefer higher speeds, long, swooping turns, soft and variable ground, or narrow tires
Now, I would just like to see the result of that serious test, to fine-tune the recommendation... |
| Here's some more stuff... | Boj
Dec 28, 2003 8:50 AM | | Earlier I wanted to find some test results where people measured rolling resistance of different sized wheels and it just so happens that at this site http://www.physics.helsinki.fi/~tlinden/rolling.html some guy has done that exact thing. Not only that but there happes to be 3 test results for EXACT same tire EXACT same model, ONLY difference in diameters. What a lucky hit!!!!!
Anyway without getting into it too much, it is possible to use those 3 entries to predice RR savings from 26" to 29" wheels. I have done that below:
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It doesn't matter what tires or surface the original test was on because we only want the relationship btw RR and wheel size. I have used 3 methods to approximate this relationship and used average of those 3 as a result. Incidentally the tests and transplantation of them into 26" v 29" application shows 11.2% reduction in RR going from 26" to 29" = pretty damn accurate to what would be expected.
Anyway the initial value of Cr = 0.03 for 26" wheel I got from earlier. There is a hillclimb I do around here of known grade, distance and time it takes me to climb it. It takes me around 7 mins to do it and similar duration of effort on the trainer I do at ~280W. Using equation from my previous post it is possible to calculate Cr and for 270W - 290W it is Cr = 0.028 - 0.032 so 0.03 should be OK.
Anyway using this data it is possible now to calculate how much a 29" bike would be faster on a given track (ignoring differences due to braking and cornering), but I'll do this later. Sleep now. |
| again, great stuff! | n8ofire
Dec 28, 2003 10:18 AM | | This is a slightly different topic, but I have long been interested how various tire pressures relate to rolling resistance, as I seem to roll easier off road with LOWER pressures. The charts indicate that the opposite should be true. Perhaps we are talking about two different things here...Rolling resistance vs Rolling ease??? (of course, this would mainly apply to rough surfaces.) Even with road bike tires, companies like ZIPP have done studies showing that more tire pressure is not always better since too much pressure results in the tire "chattering" along instead of maintaining smooth contact with the ground. Anyone have data or documented experience with different pressures? Maybe it also depends on wheel diameter, width? Thanks to all who contibute. |
| again, great stuff! | Cloxxki
Dec 28, 2003 12:25 PM | | On the beach, when the surface is close to concrete, high tire pressures make you fly.
If it's softer sand, where your feet would leave deep prints, you want really soft tires, that have a bigger FOOTPRINT, and ths sink less deep than a hi-psi tire that cuts just through. I think the amount of sand (soil) moved per meter travelled counts.
Over 3cm high Paris-Roubaix style pavement stones, I'd try a fat tire at soft pressure, so it can easily take up all the 3cm and send as little as vibration to the handlebar and seat. I think a good suptle tire has a lower internal rolling resistance at low psi than a high-psi one that goes into a high-frequency bounce over it all. Also, a wheel that doesn't touch the ground, will not be propelled, only loses speed before it again "lands".
Imagine going up a short real bumpy climb that requires momentum to reach the top, big fat soft tires will roll just up is, narrow high-psi ones will come to an early dead stop halfway.
Traction and grip also count. In CX racing, if you don't hit the rims once a lap, your tires are pumped up too much. You'll miss out on traction and grip, lose prescious time. The rolling resistance from the tire itself folding under your weight is a fraction of the wattage of working through the constant mud and spreading the air in front of you at 30+kph. 1kph of faster cornering is worth a lot of rolling resistance. Making that one tricky climb sure beats walking up it in lack of traction.
I think tire technology will have affected this whole deal now that tires roll so well at lower pressurs. A 26x2.35" Fast Fred just rolls like mad a 1.7 bar, grips like tubular glue and offers the ride of a limosine. So what if at 4bar it rolls just that little bit faster on the asphalt straight, where rolling resistance is only 20-30% of the total. |
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