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Let's say I was going to design a bike frame for a specific size of individual. I'd start with some basic frame geometries, then I assume I'd calculate the necessary member sizes, stiffnesses, etc. by calculating the force on each member in a number of standard load scenarios (i.e. maximum force applied during standing pedaling, force on seat tube when sitting, cornering at high speeds, braking, etc.) Given these forces, I'd be able to correctly size each tube/member.

My question is: what are reasonable forces to be used in these load scenarios? I assume there are some standard forces used by bicycle designers for different load cases, but thus far I haven't been able to find these loads.

(For context not relevant for this question but perhaps of interest to the casual reader, I'd like to use these forces and a generative design-based software tool (Autodesk Fusion360) to design a bike frame that is near optimal for someone of my size and desired riding style. Probably will eventually try to machine said frame from wood. I know this is not a mainstream material choice but has been used to pretty good effect here).

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  • 3
    It's all in Bicycles and Tricycles by Sharp. Hopefully someone will be able to provide useful cliff notes as an answer. Jan 19 at 20:33
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    Gotcha. My math background is pretty low but the Sharp book is often cited as one of the more accessible complete sources of that information. I believe it's all in there in a form that's pretty directly applicable to the bikes of today unless again they're less tube-to-tube-ish. Bicycling Science by Wilson has some of the same with easier language, but is less "hard" and may ultimately be less useful. I understand that getting book titles thrown at you may not feel useful, but the other side of it is that it's an area where a lot of the other knowledge out there is proprietary. Good luck! Jan 19 at 23:16
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    What you are asking for is a secret sauce of the bike industry. The forces in ordinary situations you describe are pretty easy to calculate, but to make a worthwhile dependable frame, it needs to be overbuilt, but not so overbuilt it's too heavy. That trade-off balancing act isn't simple. In any case, I think what might be best would be to design a bike frame from metal as though you were a custom framebuilder, using common tubing sizes, which has a bit of those practical trade-offs built into the tubing selection, then redesign the bike in wood, selecting tube profiles Jan 19 at 23:30
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    You know how much you weigh. Figure it out! (Note, though, that you do need to take into account "dynamic" forces from, eg, hitting a bump. But these can be calculated by knowing acceleration, etc -- stuff that you need to have a general understanding of in any event.) Jan 19 at 23:48
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    Wood could be good, but the joints (and joints to metal parts) will be the hard bits
    – Chris H
    Jan 20 at 9:13
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What you are asking is engineering. Even if you can calculate the correct thickness for all "reasonable" impacts and forces thrown at a bicycle, you still need to take into account that the bicycle will be used, so the material will undergo hysteresis.

A frame can stand a single impact providing a force of X, but it may fail after one hundred impacts of smaller force X/1000 (yes, you are reading correct, standing a single impact of force X, but failing after a cumulative impact force of 1/10 of X). If you then bring into the picture a material that evolves with time, like wood, you should expect ... a lot of trial and error.

An example: you draw your ideal wood bike, knowing the tensile strength and other parameters of wood you calculate that the top tube should be long 30cm, have a diameter 1.8 cm and a thickness of 2 mm. However, with the use you realize that such a tube will produce some resonance and some vibration, so for some unlucky reasons hysteresis will cause the connection of the seat stays (calculated to be long 22 cm, diameter 1.2 cm, thickness 1.9 mm) to fail on average after 500 km. You try to reinforce the connection, but the solution maybe is just to have a top tube with a larger diameter, or shorter, to dampen the vibrations/resonance.

How to proceed? you have two choices:

[scientific/industrial approach]

[empirical approach]

  • you take some frame building courses, where you get the experience of learning by doing, so you have a "feeling" for what is the right thickness/shape/angles etcetc.

It is not that the calculation of forces is complex or there are industrial secret preventing us from its understanding (well, there are industrial secrets on why a certain thing is built a certain way, but physics is not an industrial secret :D ). The fact is that we have a very rough understanding of reality and forces at the microscopic scale, but we can obtain insight on the resulting macroscopic behavior of materials only via:

Kestrel co-owner Preston Sandusky credits the low weight to the bike's "modular monocoque" frame, fabricated from three individually bladder-molded parts: the triangular front frame, and two two-pronged, U-shaped forks, which form the seat stay section (running from the top of the seat tube to the rear wheel dropouts) and chain stay section (from the bottom of the seat tube to the rear dropouts). Developed by former aerospace engineers at Kestrel's headquarters in Santa Cruz, Calif., U.S.A., using Pro-ENGINEER and RHINO 3-D Solid Modeling software (PTC, Needham, Mass., U.S.A.), the frame structures are fabricated

  • via empirical reasoning (Columbus steel tubes works great to build a bicycle with drops, why? because it does! )

I would NOT be surprised if, after doing some calculation based on very simple principle, you would find out that a steel frame with thickness 0.1mm and a weight of 500 grams would be able to stand all the forces related to a standard cycling scenarios.

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  • But then, how can anyone correctly calculate sufficient dimensions for objects in civil engineering, aerospace engineering, automotive etc. etc.? Isn’t the first step always to get a set of forces and then design an appropriate structure?
    – Michael
    Jan 20 at 14:13
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    @Michael Have you noticed how in the last 30 years all the bridges are the same, all the airplanes look similar (check the various iterations of B737 wrt the Comac C919 wrt the Airbus A321 ... they are wildly less different than the first passenger jet airplanes)? So there are two aspects to consider: - a lot of engineering is based on empirical formula ... which are true because they stand the test of time; - safety factors: a steel frame of 500gr would support you, but steel frame are generally around 2kg to last many more hysteresis cycles... en.wikipedia.org/wiki/Overengineering
    – EarlGrey
    Jan 20 at 14:57
  • @EarlGray: But you can model/specify load cycles as well. Afaik revolutions in airplane design haven’t happened because they are too expensive (maybe because of safety), it’s easier, cheaper and safer to iterate on the same design.
    – Michael
    Jan 20 at 16:26
  • You can model/specify forces and load cycles on untested material or untested structures, but they will be representative only if you already have data, and data come form intensive testing and ... usage! It's easier, cheaper and safer to consider hysteresis and to calculate forces acting on the same design, using the same material. What you call "design" is simply equal to "to consider hysteresis and to calculate forces acting on the same structure, using the same material".
    – EarlGrey
    Jan 20 at 17:23
  • But OP is asking for forces, load cycles etc. I guess one could build a “traditional” diamond frame, attach a lot of strain gauges and measure real world data, but certainly someone has done that already?
    – Michael
    Jan 20 at 17:50
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After reviewing some of the recommended sources above and giving the matter some thought myself, I came up with the following load cases for a hardtail mountain bike. These are by no means definitive but should cover the vast majority of normal use cases. I'll apply a factor of safety (probably 2.0) on top of the resulting calculations:

Normal Use Load Cases:

  • Full effort standing start - assume 150% rider weight applied to one pedal, 25% rider weight upwards force applied to other pedal, and remainder of upwards force applied at handlebars
  • Steady state pedaling - assume rider weight distributed between pedals and seat, applying say 400 watts of power.
  • Climbing force - same as standing effort but with a 20% incline
  • Cornering force - assume 1G (2 x rider weight) applied to pedals
  • Front braking force - not exactly sure what I'll use here
  • Rear braking force - apply maximum force before skid to rear disc caliper mounts based on a reasonable coefficient of friction for the tire and standard weight distribution
  • Jump landing force - assume a 3-foot vertical drop onto both wheels, with 80% of rider weight on pedals. (Assume rigid fork) Bike and rider decelerate in a distance equal to tire distance from rim.
  • Maximum seat force - 3 x rider weight applied to seat tube, roughly simulates going off a drop and landing on the seat

Frame resilience tests:

  • Frontal impact on fork - apply a 200 pound force at the front dropouts in the direction of the back of the bike
  • Bottom Bracket Pull Test - essentially hang a 750 lb weight from the bottom bracket
  • Rear Stay Stiffness Test - apply a 30 lb force along the axis of the rear axle to one rear stay
  • Torsional Test - apply 100% rider weight to one pedal to create a moment while fixing the head tube (to simulate frame torsion between pedal and handlebars)
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