Drops: Calculating landing force

A mechanical engineer wants to know how I calculated the impact forces for a bike drop. Yikes, here goes …

Greetings! I’ve been really enjoying your site. I’m working on getting a 2005 Enduro, and whilst doing a search at lunchtime came upon your fine pages. I’ve enjoyed reading reports of rides you’ve done in places I’ve been, especially Moab (Porcupine Rim and Slickrock, ridden on a ’97 Schwinn Homegrown FS), and your dirt biking article was great, too. I had the chance to take my XR600 to a 24 Hours of Moab race a few years back, and rode lots of great trails in the Behind-the-Rocks area while waiting for my friends to ride themselves sick.

What really got my attention was your article on doing drops. For my senior project in getting a mechanical engineering degree, I had to chance to work with Chris Titus (actually, a guy named Travis, their drafter) on doing some FEA and analysis on what was then their new DH bike, the SuperMoto. They wanted to know what would happen if a 200 pound rider landed on the seat from a 5 foot drop. To come up with some sort of realistic answer I first created a solid model of the frame using a program called Pro/Engineer, then subjected it to various stresses to see how it would react. I also did a lot of calculations and computer programming to figure out the effect of frame stiffness, spring deflection, and shock absorber effect on how much absorption took place, versus shock transmitted to the rider. What I found out is that this is a VERY complex system, with a lot of variables that have a marked effect on the answers I got.

When I saw your graph, it kind of gave me a start, because it looked very much like some of the graphs I came up with, after a LOT of work and calculations using second order differential equations to model the shock absorber. I’m very curious about how you came up your graph, and would love it if you could share your methods with me. I finally finished the project (I could email you a copy, if you were REALLY interested) and graduated, but I’m still curious about the subject. There was a lot more I could have done, and someday would like to.

So any thoughts you may have on the subject would be most welcome, and especially any technical info you could share!

Thanks again for a great site!

Tim Gates

Burlington, WA

Download this nifty Excel calculator.

Hey Tim.

Dude, I’m a liberal arts major — I’ve never even heard of a second order differential equation!

Sounds like you were interested in the amount of force and how it interacted with different parts of the bike. I just wanted to calculate the total force and see how different styles of landing (stiff or loose) affect the average impact force. As I found, it’s far better to absorb the impact than to stiff-arm it.

I stuck with the basics:

1. You get the impact velocity (v) from the starting height (h) and the rate of acceleration due to gravity (g), which as you know is 9.8 meters per second squared.

2. You get the total kinetic energy (KE) from the impact velocity (v) and the mass of the object (m). That gives you the total amount of energy going into the landing.

3. To figure out the average impact force (IF), you divide the kinetic energy (KE) by the distance traveled after impact (d).

If you land stiffly, all of the impact energy gets expressed at once — ouch! If you use your arms, legs and suspension, that energy gets spread over time, and the forces are greatly reduced. In my simulation of the 200-pound rider dropping five feet, the stiff landing created 3,000 pounds of force, while the smooth landing yielded only 600 pounds. That’s a big difference! Here’s the story.

I made an Excel calculator that’s really easy to use. Download it here. Yes, nerd style!

Tim, I know this is really simple, but I hope it makes sense to you. Thanks for the props, and keep calculating!

— Lee

I learned a lot from the HyperPhysics site.

10 replies
  1. Steve says:

    Lee it’s a bit complicated, cause at the beginning(on the edge of the drop) you have only potential energy which is Epot=m*g*h , which will be the same amount but converted into kinetic energy, cause there is no energy discipation (well not that much it would count) Epot=Ekin, and you can divide that with the distance that your limbs made, so its Fimp=m*g*h/d . So you shouldn’t even think about velocity at all (You get it from your theory too v=sqr(2*g*h) write into KE=1/2*m*2*g*h=m*g*h , tattaram ).Sorry for this boredomeness but i had to write it down 😛
    So for Tim i would like to receive a copy of your project cause I’m REALLY interested in it!!! Here is my mail : DHpinner@gmail.com
    And here is a link for you to get you going, http://www.mtbcomprador.com/content/category/3/67/105/
    It basically deals wit path analysis but it is a good starting point for your further interests and a pretty neat reading if you wanna get trhrough it all, good luck for that!

  2. Gille Briand says:

    I think the calculations are way more complicated then that. I remember from my dynamics courses that you need the time of impact to get the average force. That could be find with a good video camera with alot of frames per seconds.

    I think Tim used the time he derived from his equations. The second order differential equations are often used to model a spring system. So he could find the time of impact knowing the mass and other variables. Think about it in term of oscilations.

    In another course ( machines ), for calculating impact with used a formula that looked like this: Fi: W(1+(1+(nV^2/gd)^1/2)
    where Fi is the impact force in Newtons
    W is the weight in kgs
    n is a coeficient of dissipation usualy = 1
    V is the speed in m/s
    g is 9.8m/s^2
    d is the static deflections when no impact : could be complex to figure out

    Maybe your basic physics are acurate. The two methods i described were shown to us very quickly as it will be seen in more details in other courses.
    But if anyone is interested……i could ask my university teachers about it.

    Also i am very interested by your research tim. if you want you can send it to me

    This is actually a great topic. Might be useful in two years when i do my gratuate project.

  3. leelikesbikes says:

    There’s no doubt my math leaves a LOT out. Dynamics within the bike, mass of rider vs. bike, mass of sprung vs. unsprung parts of the bike, mass of sprung vs. unsprung parts of the rider (head and torso vs. arms and legs) … It goes on and on …

    A can of worms.

  4. Tage says:

    I like lee’s approach. Clearly you can get into weight distribution, travel, damping, etc… But to be concise is usually best.

    Furthermore, isn’t this math childs play for an engineer? I could figure this out on my own, and I’m only a senior in high school.

  5. Curtis says:

    This is not childs play at all. The simple physics equations are, however, if you want real data that you can design something from, it’s far more complicated that that. Gille summed it up best. First of all, modeling a real life situation with differential equations (partial, linear, or non-linear, 2nd degree, or 3rd degree etc…) is very very complex. To account for every last detail, the many, many, many equations would come out rediculous. And at the same time, solving these equations accurately is even harder. Yes there are computer programs that can do this, however, every good engineer/mathematician knows that hand calculations are the only way to back up what you programmed your computer to do. And it is just that, a model. It is not an exact description of what is happening in real life.

    …oh, and don’t forget to subtract the energy absorbed by the total drag force (pressure and friction). even though air has a relatively low density, it can still be included.

  6. Anthony says:

    It’s easy to calculate how much energy is absorbed upon landing, but to correctly calculate the peak *force* you will need to know all the variables that will affect the suspension’s travel on landing. The suspension will absorb the energy by applying a reaction force over a distance (work), the key is to determine this distance, or the suspension travel. In order to do this you need to know these parameters: damping and spring constants for the front and rear suspension. Unless you can dyno test them you will need to assume them. You will also need to know where your center of mass will be on landing, and angle of incidence of landing as these affect the bias between front and rear. You will also need to model the human body as a spring/damping system! I think you will find that the human will disperse much of the energy, therefore reducing the peak load. Good luck modeling the human. The bicycle’s frame should probably be modeled as a rigid body (relatively to everything else it is rigid, this is a safe, conservative assumption). Don’t forget the tires and wheels…My point is that after you are all done doing this you have probably made so many assumptions that the result has little relevance. An easier way to determine peak loading would be experimental: instrument the bike. Take advantage of the suspension elements and use them as in-line load cells. A time based measurement of the front and rear shock travel simultaneously sampled would be pretty good. Knowing your spring constants for the front and rear shock will give you a pretty good idea. you will need to assume damping constants, but they most likely add little to the peak load. You will also need to know the angle of incidence of the landing. This can be tricky, but a video may help and if you are close it should be good enough.

    Without data acquisition equipment, you could come up with a crude conservative estimate by measuring your front and rear shock maximum travel after the impact (use the old zip-tie trick). It is pretty easy to determine your spring constants the rear spring usually has it printed on itself. You will be omitting damping forces. You will also be assuming the maximum travel front and rear was attained simultaneously, it’s not necessarily true, but it’s conservative.

  7. Andrew says:

    Who cares about that stuff if you’re not designing a new frame or something yoursel? All you need to know is that landing smoothly will make your bike happier (I broke my rear axle off a 4 foot drop). Then I read Lee’s book and stuff isn’t breaking as often anymore…

    I definitely prefer the sane way to figure out impact force, IF+KE/d!

  8. gigioconio says:

    Hi im from Chile (south south america), and I make my graduate book for mechanical engineer, so im doing a optimisation for the rear suspension sistem of a bike, so let me teel you that is extremely dificult to calculate, the landing force; Yes we can make a simplification, we need the time of the impact, that can be 0.1 or 0.2 seconds.
    So im very insteresting in the Tim project so could anybody send me that information, I will be very happy if I have that.
    I make a simulation whit Proengineer, but I have a lot answers that I could not response yet.
    I cans send you mi proe files whit a simulation, of a bike in a drop of two meters.

    Many many thanks to the site

  9. Murali krishna says:

    Dear All
    I am in search of a process of caluclation of load of bicycle. I found this forum discusing on my issues. Hence dropping a message and expecting a quick responce. Thanks in advance.
    1. I am designing a electrical motor for Electric bike application- Hub type. Hence for analysis purpose I need the motor mechanical parameters like Moment of Inertia, Attenuation constant and Frictional constant. I want the procedure of calculation of these particular parameters.
    2. The load on cycle is another parameter. The motor which I am designing is for person weighing 100 kg . The wheel size is 16 inch. So I need to calculate the torque or power required by the motor to overcome this load. Pls help me to get this . this is important specification for by design.

    Thanking you. Pls email me this solution to murali@naver.com .

    I may not be able to visit this site again.

    Thanking you
    With best regards

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