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Question on speed, weight and climbing(31 posts)

Question on speed, weight and climbingLLSmith
Nov 6, 2002 1:44 PM
Two riders with the same ability climb the same five mile hill. Both bikes have the same components.Rider A is 165 lbs. and riding a bike with an older steel frame that weighs in at a total of 22 pounds. Rider B is 172 pounds, but riding a new bike that weighs in at 15 pounds.Will they both get to the top at the same time?
I think the answer is yesirregardless
Nov 6, 2002 2:31 PM
assuming the same bottom bracket stiffness.
and assuming the same rotating wheel weightirregardless
Nov 6, 2002 2:32 PM
but that was implied by your statement that the bikes have the same components.
Rotating weight has nothing to do with itKerry
Nov 6, 2002 4:17 PM
Once the rotating mass is up to speed, there is no difference in the amount of work to climb a hill. Even if the rider's speed is oscillating, a heavier wheel will both take more energy to accelerate and give up more energy when decelerating, so the effect cancels out. It's simple physics, nothing more. If two riders have the same power delivered to the pedals and same drive train efficiency, they will take the same amount of time to haul the same TOTAL weight up the hill. Full stop.
Not exactlyirregardless
Nov 6, 2002 6:21 PM
Where do you think the energy goes when you decelerate with each half stroke going up a hill? Not back to your legs. Your legs aren't springs that capture that released energy. If that was true you could climb hills for days after one pedal stroke. The accelerations and decelerations don't simply "cancel out," as you put it.

Hill climbing is different than going on the flat. On the flats, I agree with you that once up to speed, rotational weight doesn't matter. But that's not true going up a hill.

go here:

make the standard rider 2 kgs heavier than the test rider but make the test rider's front and rear wheels 1 kg each heavier than those of the standard rider (an extreme example, but good for demonstration purposes). The model shows that the rider with the lower mass wheels is faster, which wouldn't be the case if rotating weight didn't matter.
Nov 6, 2002 7:22 PM
I stand corrected, you are right that once up to speed rotating mass doesn't make a difference even, even going up a hill. The problem, however, is the "once up to speed" assumption. If there are small accelerations/decelerations, as there are on each pedal stroke for most people going up a steep hill, then this doesn't hold true. And the energy lost on the decelerations is not recaptured.

The analytic cylcing model didn't make the point I thought it did when all of the other wheel stats were accounted for. But again, it assumes a constant speed and doesn't take into account the small accelerations and decelerations that most people have with each pedal stroke.
OK, that's officially the geekiest bike related site I've seenjoekm
Nov 7, 2002 5:51 AM
The problem with the "once up to speed" argument...mmquest
Nov 6, 2002 8:11 PM
is that you never get a bike (or anything in the real world, for that matter) "up to speed." In an ideal situation if you were riding on a flat with no friction (think wind, bearings, etc.) this argument would work and, once up to speed, weight wouldn't matter. However, in the real world you must contend with a constant deceleration caused by friction...otherwise, on a flat, you wouldn't ever have to pedal. Furthermore, on a hill, there is also a deceleration due to the slope of the hill.

Making a long story short, when we are riding, we are constantly accelerating to overcome the negative accelerations due to friction and gravitational forces.

Therefore, since the rider with the lighter bike would have to do less work accelerating the heavier bike up the hill, (s)he would have my vote.

Also, interesting to note that we are all assuming that the wheels on the heavier bike are also heavier. If, in fact, the two bike's weight only differed for non-rotating items (handlebars, frame, etc.), then each rider should reach the top at the same time.
Rider B*UncleMoe
Nov 6, 2002 2:35 PM
Rider B will get to the top first. He is heavier and has experience carrying his weight around. The lighter bike feels nimble and quick beneath him.

THe 165 rider feels the 22 pounds of bike underneath him as it represents a larger percentage of his own weight.

* This response assumes this is the first time either of these two riders are actually riding the bikes in this problem. If these were the riders regular bikes, and they both have the same ability to climb, one must assume that "ability to climb" was based on statistics of these riders on their regular bikes.

I agree Rider BLC
Nov 6, 2002 2:55 PM
Since you said they both have the same climbing ability which really is strength to weight ratio, then the difference would be the bike.
And you'd have to further assume ...Allez Rouge
Nov 6, 2002 2:42 PM
... that they climb the hill in the same gear, at the same cadence. Also that tire pressures are absolutely identical and a host of other factors. But I think what you are getting at is: if the total weight of each bike/rider is identical, but distributed differently, will two riders of equal ability climb at exactly the same rate? The answer, all else being equal, is Yes. Both riders have to pedal 187lbs worth of bike and body up the hill. It doesn't matter how the weight is distributed.
they would crest at the same timeniteschaos
Nov 6, 2002 3:56 PM
It is simple. If rider A and B have the same power, and their total mass (rider plus machine) is the same, then they have the same power/weight ratio and will climb the same. That is assuming everything else is the same (like rotational mass). Static mass is static mass, doesn't matter where it is located.\
Nov 6, 2002 6:19 PM
So if both riders have equal power and equal total weight then the only difference is the distribution of that weight. Rider A has more weight closer to the ground and rider B has more weight higher up then (here is a question for the physisists) are they equally suseptable to gravitational pull? And does the slope of the hill make a difference? is it just as easy to push weight that is closer to the grounnd as it is to push higer distributed weight up a given slope?
Nov 6, 2002 7:42 PM
Gravity pull on all opjects is the same weither it is a paper clip or a 2,000 pount car

Assuming the riders have the same ability to climb
- this must be based on some standardized measurement
their body weight would be unimportant because they both have the same ability to climb

They also have the same parts so the only factor would be the frame- disreguarding wind resistance and other unimportant factors

Therefore the one with the better frame will win, it is lighter, and likely more rigid.
Nov 6, 2002 9:47 PM
weight distribution matters, and i can prove it with an extreme case...

you're riding up a slope, and you center of gravity can be in 3 places... 1) behind the rear wheel, 2) just over the rear wheel and 3) in front of the rear wheel.

1) you tip over backwards
2) you'll have to limit your power output so your don't tip over backward.
3) you can still tip ourself over backwards if you produce enough power, but this is unlikely the more your CG is in front of your rear wheel.

now prove to yourself that by simply raising your center of gravity that these 3 situations are possible. aka if your CG was a mile up, it'd definitely be case 1.

but again, i don't think this really affects much in the real world, unless you're doing some really steep hills.

Hey Frithniteschaos
Nov 7, 2002 8:42 AM
this is basically a Physics 1 level question. Read up on some basic Projectile Physics and you would find it very educational.
Not sure if there's a correlation here, butB2
Nov 6, 2002 7:54 PM
I know when you carry a pack with a poor center of gravity, it's takes a lot more effort. As the pack grows in volume, the center of gravity of the pack moves further away from your body. The further the CG is away from your body, the more difficult it is to carry.

Now here's where it becomes a bit of a stretch. Wouldn't the person carrying more weight closer to their body (i.e. on their body) expend less engery to move around assuming all else equal? I guess I really don't know the answer - just asking the question.

Then what about this???REPO42
Nov 6, 2002 11:05 PM
both riders decide to walk there bikes up the same hill at the same speed under the same circumstances as above(I know how lame this sounds, but one can relate better to pushing something up a hill as opposed to riding) who would get to the top first? They would get there at the same time, right? So I think the question would be better stated as who would expend the most energy to get to the top? Wouldn't the person riding the heavier bike expend more energy than the rider on the lighter one?
Then what about this???Allez Rouge
Nov 7, 2002 6:12 AM
REPO42 asks: Wouldn't the person riding the heavier bike expend more energy than the rider on the lighter one?

That depends. Are you still going with the original stipulation that the rider on the lighter bike weighs more? If so, then the answer is NO, because energy must be expended to get BOTH the weight of the bike AND and the weight of the rider up the hill. Any advantage gained by having a lighter bike is offset by the disadvantage of having a heavier body.
I think the answer to this one is yesLLSmith
Nov 7, 2002 6:50 AM
Competitors doing endurance races want the lightest equipment possible. If you have to get off and carry your bike you would use less energy with a 15 # bike.
Maybe, but I don't think soAllez Rouge
Nov 7, 2002 7:10 AM
There's no question that it takes less energy to carry (or pedal, or push) a 15lb bike up a hill than a 22lb bike. But I thought we were talking about a hypothetical problem involving the TOTAL weight of the bike and rider, and in which the physical abilities of the riders are the same even though their body weights are not.

Look at it this way: if a rider unbolted his crank arms and put them in his jersey pockets, the bike itself is now lighter. But will it be any easier for the guy to get up the hill?
Maybe, but I don't think soLLSmith
Nov 7, 2002 7:34 AM
OK, I forgot everything but the bike and rider were the same.How about if one person was both riders.Lets say I lost 7 pounds, but got a new bike that was 7 pounds heavier.Assume that my ability did not change. Would I get to the top in the same time as when I was heavier, but with a lighter bike?
Maybe, but I don't think soLLSmith
Nov 7, 2002 7:43 AM
The answer must be yes since the total weight is still the same.
I think the answer is YES, too, but ...Allez Rouge
Nov 7, 2002 8:23 AM
... now we're getting into that "all else being equal" area in which it becomes increasingly difficult to figure out if all else truly IS equal. Specifically: what is this extra seven pounds you just gained? Is it all fat -- dead weight around your middle -- or is it muscle that might help you climb better? Or a mix of both? We've reached the point where we're splitting hairs that have already been split two or three times.

IMO you're on the right track with your "How about if both riders was one person" approach, but I would take it even further and eliminate any variations in the rider altogether. That's why I used the example of 10 pounds of ballast being the same whether it's in your jersey pocket or strapped to your bike. That is probably as close as you are ever going to get to being able to make a direct comparison between adding extra weight to the rider vs. adding the extra weight to the bike.
This is really a Biomechanics questionniteschaos
Nov 7, 2002 8:47 AM
With man-machine interactions inertia should be studied. In bikes it isn't as important as in motorcycles because most bikes are fairly light compared to the human riding them. With motorcycles though, there is a large push to "center the mass" of the bikes, even if it means raising the center of gravity a bit, so that it can be "flicked" into corners faster. Well, that was how it was explained to me by Yamaha Motorworks.
On further review ...Allez Rouge
Nov 7, 2002 5:43 AM
... those who are saying Rider B would get to the top first may be right. It all depends on how you interpret the question.

I assumed the basis of the question was simply this: if the total weights of two bike/rider combinations is exactly the same, does it matter if the weight is distributed differently? The answer is NO. Think of it this way ... if someone decided to make you carry 10 pounds of ballast to slow you down, would it matter if you put it in your jersey pocket or strapped it to your bike's frame? No, it wouldn't.

But if you take the original setup literally -- "Two riders with the same ability" -- then the situation may change. One rider is seven pounds heavier than the other, but so what? The stipulation is that they have equal ABILITY, not equal BODY WEIGHT. So the implication here is that if you put both riders on identical 22lb bikes, they should still climb at exactly the same rate because (a) they still have equal ability, (b) the difference in their body weights is still the same, and (c) the bikes weigh the same. Put the riders on identical 15lb bikes and, again, they'll climb at the same rate because nothing else has changed. But if you put the heavier rider on the lighter bike, he now has the advantage. He started out being able to climb right with the lighter rider despite his heavier body weight. Give him the lighter bike, and he will get to the top first.

Again, the "correct" answer is going to depend on one's interpetation of the question. If the riders are equal independent of their bikes, is a lighter bike an advantage? YES. If the riders are equal when compared on these two particular bikes, does it matter that the total weight of each bike and rider is distributed differently? NO.
I vote for this answer!Brooks
Nov 7, 2002 10:57 AM
Ability = strength/weight ratio on same bikes. Vary the bike weight and the lightest bike gets to the top first to drink the beer that JS Haiku has waiting.
The 172 lb rider will be much faster, here's why....rwbadley
Nov 7, 2002 7:59 AM
You state they are both in exact same condition or ability. What this means to me is that if each is on a bike that is the same percentage of body weight they reach the top at the same time. The 165 lb rider is on a bike that is 13.33% of body weight (@22lbs) The 172 lb rider will need to be on a bike @ 22.92 lbs for same condition.

Now, you take almost eight lbs off the 172 pounders bike, the percentage of bike weight for the 172 pounder is now only 8.57%

The 172 pounder should cream the 165 pounder to the top, by a fairly subastantial margin.. (I don't have the time, but go to analytic cycling to figure the margin)

Math and physics were never my strong suits ...Allez Rouge
Nov 7, 2002 9:00 AM
... but I genuinely do not understand what the weight of the bike, expressed as a percentage of the rider's body weight, has to do with it. The percentage figures make for interesting reading but it seems to me that total weight of the bike/rider combo is all that matters.
is there beer at the top? nmJS Haiku Shop
Nov 7, 2002 9:24 AM
another way to roadie
Nov 7, 2002 11:58 AM
Assuming I'm on the same bike, which way would I ride up hill faster:

A) wearing a Camelback that weighs 2kg, but a bare frame?
B) With 2kg worth of water bottles and seatbag tools?

Total weight (static and rotating) is the same, the only real difference is effective frame weight vs body weight.

The answer probably is that it really won't make any measurable difference, compared to other factors that affect even the same rider doing the same climb on the same bike on two different days.