# B If the pedal crank arm length of a bicycle increases....

#### RipVanCalcNoob

You have 2 bikes. They only differ in 1 way.
The length of the crank arm (where pedal attaches)
https://en.wikipedia.org/wiki/Crankset

How will these bikes differ when riding?
Is one harder to pedal than the other? Why?

Related Other Physics Topics News on Phys.org

#### BvU

Homework Helper
Hi Rip,

Make an assumption !
If one crank is twice as long as the other, with which one can you deliver more torque ?
And with which one you have to press over a longer distance ?

#### sophiecentaur

Gold Member
Is one harder to pedal than the other? Why?
What are your own views on this? PF gives better responses when questioners contribute with their own input. Try it.

BvU

#### zakeen

Interesting....

So if the same amount of force is applied on the pedal axis. Then the longer crank should produce more torque?

Some argue, that while the shorter crank will require more force for the same amount of torque to be produced on a longer crank, then the shorter crank can simply switch to a lighter gear(talking bicycle) to offset the more force applied. But I argue that ok, it will make the workload(force being applied the same) but with smaller gear, your rollout will be shorter, meaning you will be going slower.

Some argue, that on a longer crank you have a slower RPM which is also not good. But I argue, the RPM might be slower(or the number of RPM might be less) but the leg speed, the speed of the axel of the pedal will be moving faster because of the long distance it must travel for the same rotation. In this sense, you are not really moving slower, even though your RPM is less. But also, if it takes you less time, to do a full RPM at the same speed, you are not behind, but you are longer in the pedal stroke where you produce the most amount of force(1-O'Clock to say 6 - O'Clock.)

I would really like people to argue my points and say I am wrong and give reasons please. Because I want to understand it more and no one really knows from what I have seen...... These are just my theories but people always seem shorter cranks are faster......

#### sophiecentaur

Gold Member
You would need to consider the geometries of individual cyclists if you want to find a 'best' combination. Long and short femurs would require different grand lengths if what really counts is the length of action of muscle fibres. If you look at films of groups of cyclists, you see a range of pedalling speeds and, if they are high performance cyclists, they will be using near optimum individual bike geometries for them. IN a simple analysis, they would all be pedalling at the same rate.
Geometry is only one of the factors that vary with cyclists and what is needed is to strike a balance between Power Output and Efficiency. Bike and rider would need to be matched to achieve that.

#### zakeen

Let's put the rider out of it for this topic as there are too many variables out of our control. What's your theory. I'm interested because in Pro Cycling world. I think they have no idea....

#### sophiecentaur

Gold Member
Let's put the rider out of it for this topic as there are too many variables out of our control. What's your theory. I'm interested because in Pro Cycling world. I think they have no idea....
How is that a useful approach? Would you suggest designing a racing car transmission without including the engine characteristics? If the Pro cycling world has "no idea" then they clearly haven't chosen to use an analysis that's so blatantly over-simplified as the one you propose. It can yield very little, if anything, to help towards getting 'the perfect bike'.
PF is continually getting posts from sportspeople with requests to use Physics usefully but in a very simple way. The simple Physics of Machines is totally inadequate to describe Boxing, Batting, Throwing or Working Out because it doesn't deal with Muscles and CV systems.
It may be unsatisfactory but there doesn't seem to be substitute for the well informed pro-sportsperson or coach.

#### zakeen

How is it useful? Well. I guess I am trying to start from the basics. Google crank length and I am empty handed in proper information. When I hear that having a shorter crank will require more Nm then a longer crank and changing to a smaller gear will offset that I role my eyes.... because an easier gear means you're going slower.... when Nm is the same. Nm is the amount of force the rider is pushing on the cranks.

I've done courses in bike fits and unless a crank is too long reducing you hip angle flexition too much then I haven't been taught anything from a performance point. Just shorter is better. I'm trying to understand why....

Their arguments from the best bike fitters are. You can have a higher cadence(rpm) but in my opinion rpm is only the rotation number. Rpm doesn't equal to leg speed. Further away from the bottom bracket(pivot point) you increase your leg speed. If two riders have the same leg speed and one has a slower RPM because of longer crank then that rider has less time at 12 o'clock and 6 o'clock times when you produce zero power(not really but you get my point) and have a longer(time) period over the down stroke. If that makes sense.

I really want someone to argue with me so I understand it from a mechanical point of view. That's why I am here.

#### hutchphd

How is it useful? Well. I guess I am trying to start from the basics. Google crank length and I am empty handed in proper information. When I hear that having a shorter crank will require more Nm then a longer crank and changing to a smaller gear will offset that I role my eyes.... because an easier gear means you're going slower.... when Nm is the same. Nm is the amount of force the rider is pushing on the cranks.

I've done courses in bike fits and unless a crank is too long reducing you hip angle flexition too much then I haven't been taught anything from a performance point. Just shorter is better. I'm trying to understand why....

Their arguments from the best bike fitters are. You can have a higher cadence(rpm) but in my opinion rpm is only the rotation number. Rpm doesn't equal to leg speed. Further away from the bottom bracket(pivot point) you increase your leg speed. If two riders have the same leg speed and one has a slower RPM because of longer crank then that rider has less time at 12 o'clock and 6 o'clock times when you produce zero power(not really but you get my point) and have a longer(time) period over the down stroke. If that makes sense.

I really want someone to argue with me so I understand it from a mechanical point of view. That's why I am here.
That is noble enterprise, but you need to do some work:
1. If you wish to talk physics you need to know the language. What are the SI units for Force. Energy, Torque, and Power? Nm is not a force. Make yourself a little list
2. @sophiecentaur is correct that your questions are almost all physiologic. A bicycle takes power from the rider and efficiently does work on the road. It doesn't care whether the crank is large or small or geared up or down......as long as energy is conserved.
3. If you characterize the rider's capabilities in a meaningful way (power output, max foot force, etc,etc) then you can talk about how to optimize the system.
Perhaps write down the parameters that characterize/differentiate riders performance.

#### zakeen

I appreciate all your replies. I am here to learn that's why I am asking. I understand cda, rolling resistance, tire pressure, etc.... all play factors but sponsored equipment limit this and aero position can be achieved with adjusting crank length. I'm just failing to see why shorter cranks means more power(in form of watts, measured by powermeters). If the rider is apply the same amount of force on a crank arm, same rider different crank arm lengths and he/she is pushing down on the cranks with equal amounts of force, then which produces more watts?

Extreme differences in cranks length would be 170mm as shortest and 180mm as longest. The standard most riders use is 172.5, regardless of size.... for me personally I see a problem there as one rider might be 15% taller and if all things are equal in body proportion then the shorter rider has longer cranks in ratio to leg length than the taller rider.

But let's say you apply a 2kg force at the end of a 170mm crank and a 180mm crank. For 5 mins. Only pushing downwards on the pedalling stroke. The 170mm crank has a circumference of 1068mm. 5mins at 100 RPM has a total of 534,000mm of travel distance. For the longer 180mm crank to cover the same distance (trying to keep rider leg speed equal) only has to do 94.5 pedal strokes per minute. Over the 5mins means he/she has 25 less times at 12 o'clock and 6 o'clock position, where power is almost equal to zero. So this could also be a benifit.

So.... which is better in your opinion? To me I feel the longer crank require less energy because torque is equal to force(being applied by the cyclist) x be perpendicular distance(170mm vs 180mm) and as the longer cranks have a longer perpendicular distance to the pivot point I understand it to be easier for the cyclist.

#### sophiecentaur

Gold Member
So.... which is better in your opinion?
Better?
This is your problem. The usefulness of the machine depends on the user.
To me I feel the longer crank require less energy because torque is equal to force(being applied by the cyclist) x be perpendicular distance(170mm vs 180mm) and as the longer cranks have a longer perpendicular distance to the pivot point I understand it to be easier for the cyclist.
The Physics of this question is not a matter of feeling. You seem to be requiring an answer in your terms but the only way you will get a meaningful answer from PF is to learn what the proper terms mean. Yes - it's an annoyingly exclusive club and you can only benefit if you play by the rules and have common terms. You want to play football and you cannot use the laws of cricket.
I'm just failing to see why shorter cranks means more powe
In general it doesn't. You have seen a kid on his first bike with legs going so fast it's a blur. He cannot deliver much power because he has only one 'gear' available.

#### zakeen

Tough crowd here.....

The OP started this thread, I was also interested. I didn't create a new thread and played by normal forums rules. Searched and found a thread asking exactly what I wanted to find the answer of a question been already asked. So I asked the same question as the OP here. Even another person joined asking the same question. So 3 of us are wondering of a question asked back in 2016..... still no answer..

Better?
This is your problem. The usefulness of the machine depends on the user.
Everyone is asking the same thing, the user(rider) is the same, same energy output, but the bikes are different. Only difference everyone is asking is crank length. Same rider, different cranks. Which produces more power?

The Physics of this question is not a matter of feeling. You seem to be requiring an answer in your terms but the only way you will get a meaningful answer from PF is to learn what the proper terms mean. Yes - it's an annoyingly exclusive club and you can only benefit if you play by the rules and have common terms. You want to play football and you cannot use the laws of cricket.
You're right, it does feel like.... as you say in your words... an annoying exclusive club, everyone seems to not point me to the rules for me to play by. I see responses but no answers the OPs topic or even someone willing to help and point me to the rules that I must play by to get an answer of a question 3 people have asked on a forum site where people are coming here for help from smarter individuals. I'm here for help. Not to disturb, upset anyone. You even said to RipVanCalcNoob that they should say their views. I have, I feel from a mathematics point of view, same energy being applied a longer crank is better, but people say otherwise and I came here hoping that a smarter person will tell me why I am wrong so I understand the science of it, not just because John Smith said so....

#### hutchphd

Here's all the specific physics of bicycle locomotion:
1. Take the force of the foot on pedal
2. multiply by (crank length/tire radius)
3. multiply by (sprocket teeth/chainring teeth)
4. That is the propelling force of tire on road
5. Apply Newton's laws of motion (and aerodynamics if you wish).
There is no optimization to be made without further specific information about humans.

If one desired to attach a "leg" with "muscles" to the model, and characterize these appropriately you might start towards your idea.
I am happy just to pedal 10 miles every other day and not fall off...

#### sophiecentaur

Gold Member
Everyone is asking the same thing, the user(rider) is the same, same energy output,
But you cannot specify that the rider is producing the same energy output or the same force or the same pedalling rate. In fact, even replacing the rider with an electric motor that's somehow regulated to satisfy those conditions would be problematical.
It's harder than you are insisting it is and @hutchphd says so, too. There's no point in getting exasperated or taking offence about it. First you need to appreciate this and then you may start getting somewhere.

#### zakeen

Here's all the specific physics of bicycle locomotion:
1. Take the force of the foot on pedal
2. multiply by (crank length/tire radius)
3. multiply by (sprocket teeth/chainring teeth)
4. That is the propelling force of tire on road
5. Apply Newton's laws of motion (and aerodynamics if you wish).
There is no optimization to be made without further specific information about humans.

If one desired to attach a "leg" with "muscles" to the model, and characterize these appropriately you might start towards your idea.
I am happy just to pedal 10 miles every other day and not fall off...
Thanks Hutchphd for your response. Let's take #2 From what you said,
• multiply by (crank length/tire radius)
So if a rider is 70kg. Standing on the crank and not sitting down. All his/her weight is on the pedal axis(end of crank). There must be a difference if a crank is 170mm long compared to 180mm long if everything else reminds the same. Even the rider. The only variables that changed are the cranks length. What's your opinion?

I understand all the other factors make a difference. But let's make them the same for both situations. Just talking cranks here.

#### Steelwolf

Gold Member
One of the most basic points to remember is that the pedal crank, however long, is a Lever, with the center shaft being the fulcrum.

Apply basic lever type mechanics to a simplified view and you should come up with the answers you were looking for. Comes down to the basic principles of a lever.

Riding a 10-speed in the 70's in Hilly Puyallup and Tacoma Washington made very certain that this was one lesson I learned right. Pedal crank length and spocket diameters are like direct inputs to the Lever equations with regard to radii.

That SHOULD be enough clues to work through it, especially with what others have posted.

#### hutchphd

Not a badly stated question...!
The propelling force from the road will increase by (18/17). If she then chooses a slightly stiffer gear (by 17/18) then the dynamics will be back to the same except her feet go round in a bigger circle So which is better???? I cannot tell you without meeting the rider.
If you wish to be able to discuss these matters intelligently with your peers you need to study some physics. I of course highly recommend it!

#### jrmichler

There is a really good book on this subject: Bicycling Science, by David Gordon Wilson. It's in the third edition, and is still available on Amazon. It has 477 pages of bicycling science goodness. Highly recommended. Here is a plot of power vs crank length:

Opinions on crank length have been around since bicycles were invented. This book has the available science on the subject.

I highly recommend reading this book. You will then be able to discuss the subject intelligently. A basic high school physics background will be very helpful.

#### 256bits

Gold Member
All three supposed criteria cannot be satisfied at the same time if the back wheel receives the same torque.
Energy in == energy out.
Power == Energy / time.
If the bikes are travelling at the same velocity, the frictional resistance forces would be the same, then crank length makes no difference if energy input is the criteria.

Maybe the question should be:
For a robotic bicycle rider, with pneumatic legs, how is his riding affected by pressure, crank length?

#### zakeen

There is a really good book on this subject: Bicycling Science, by David Gordon Wilson. It's in the third edition, and is still available on Amazon. It has 477 pages of bicycling science goodness. Highly recommended. Here is a plot of power vs crank length:
View attachment 246590
Opinions on crank length have been around since bicycles were invented. This book has the available science on the subject.
Yet in the Pro's, there is no clear answer. This graph doesn't say much. Is this for a 1 second all out? Or a 10min effort? Plus while their peak is understandable for a 1 to 5 second All out Sprint. I fail to understand what the minimum represents, because even for a 10 min effort, those minimum numbers are off the charts..

Plus recumbent is not really cycling race cycling.... no offence.

All three supposed criteria cannot be satisfied at the same time if the back wheel receives the same torque.
Energy in == energy out.
Power == Energy / time.
If the bikes are travelling at the same velocity, the frictional resistance forces would be the same, then crank length makes no difference if energy input is the criteria.

Maybe the question should be:
For a robotic bicycle rider, with pneumatic legs, how is his riding affected by pressure, crank length?
Maybe the question asked should be if a robotic bicycle rider. Because when talking about cranks in different length, what is more efficient for the rider and when we are talking about energy, it's not energy at the crank that's important. It's energy the rider is spending to produce the force on the crank arm. If he/she pushes the same amount of force at different points on the crank arm it must have an impact in performance. Changing crank length in a ICE makes a different in power output. So I fail to understand why people think it doesn't make a different on a bicycle.

#### hutchphd

I'm sorry...... ICE???

Gold Member

#### sophiecentaur

Gold Member
So I fail to understand why people think it doesn't make a different on a bicycle.
Of course it makes a "difference" but the optimum is different for all users. If you cannot characterise the user then a single, two dimensional graph is unlikely to be of use. I would say that the only way to find the best crank length would be to do a vast number of experiments with different crank lengths and different gear ratios at different speeds and inclines. And that would only apply to ONE rider.
The alternative is for one rider to try a few different cranks in practice and choose which one works best for her / him. It would be the best use of time. Basing an assessment on some bogus parameter is not Physics and certainly not good Engineering.

### Want to reply to this thread?

"If the pedal crank arm length of a bicycle increases...."

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving