This version is a continuation from my two previous constructions baby & marc. The wheel base is take from Marc, even though I do not like the over-eager self centering effect to much. The front part too, is inspired from Marcs design. The rear part now complements the design.
I went back to a suspension-less bike, because its easier. When it's to hard, I can put big apple sized on the rear wheel. The above pictures are rendered with "tiogra comp pool" sized tires. The front does not have the place for a big apple.
The rear part of the bike is all out of thin tubing (mostly 10x1 and 12x1, construction steel). Lets see if it holds...
I am going to use just simple "construction steel", which is in europe known as St37. The yield strength of St37 is 235N/mm2 (for the non-technical 10N is about 1kg of weight).
|tube||area (mm2)||yield strength tube (N)||weight (kg/m)|
|round 10mm, 1mm||15||3507||xxx||0.1177|
|round 12mm, 1mm||18||4245||xxx||0.1413|
|round 1/2", 1.5mm||28.1||6617||xxx||0.2211|
What about buckling of the tube? Buckling occurs when a tube is put under pressure, it can buckle. The maximal buckling force depends on the length of the tube. The formula goes like (it's called the Euler formula):
Fmax = π2 E I / (L2 v) = c / L2
Where for tubes I = π (D4 - d4) / 64, and E = 210kN/mm2
In the following table c is calculated (for a safety factor of 2), And the maximal allowed length for a force of 3kN (300kg) and maximal allowed length at there maximum forces.
|tube||c (Nmm2)||Lmax (mm) @3kN||Lmax (mm) @yield strength|
|round 10mm, 1mm||.35M||241||223|
|round 12mm, 1mm||.62M||321||270|
|round 1/2", 1.5mm||1M||417||281|
...now I know why I need cross tubes at places! ;-) But a big worry I need not to have it seems, the largest pressure stress (see below) is between the "bottom -> front seat mount" and this is about 270mm.
The thin tubes allow the frame to be abstracted as a set of tubes connected by freely movable joints (in german: Fachwerk). This leads to a highly simplified calculation of the stresses on the frame. Simplifications:
The resulting equations are just a bunch of linear equations, which can be easily solved using a matrix calculations. Octave was used here.
I loaded it with 90N on the front seat mount, and 10N on the rear. The equatiosn are linear, so just multiply with the factors/units you like.
|name of tube||force|
|pressure||rear axle -> rear seat mount||49|
|front seat mount -> rear seat mount||54|
|bottom -> front seat mount||115|
|front seat mount -> pivot (bottom)||65|
|front seat mount -> pivot (top)||92|
|pivot -> front axle (top)||87|
|tension||rear axle -> bottom||-42|
|bottom -> rear seat mount||-48|
|bottom -> pivot||-143|
|pivot -> front axle (bottom)||-97|
Clearly a few tubes suffer, while others seem not to be loaded much!
A little experimentation also shows that:
I am using rod-end bearings. The ones I decided for are really small. They are GA 10 types. To lessen the strain on the bearings and the frame in general I have made the pivot very long: the rod-ends are placed 20cms apart. The calculation above shows the numbers. It is much lower then before (30% less force on the high strain tubes).
To make the pivot heigher I had to change the angle of the pivot. It is now on 55degrees. Also the ground distance has lessened to 9cms. I hope that is enough...
Normally the luggage bearer is only an afterthought. Here I want to have it integrated into the solution. I want to use the luggage bearer in the construction of the frame.
The thin tubing will create a "hole" under the seat, an area that can be used to transport luggage. I am going to exagerate the size of that hole, so I can come up to about 15liters, may be more. At the same time, the size of the tubing will enable me to easily attach more luggage on the outsize of the tubing.
To get to the luggage compartment, I want the seat removable. The seat will be an inspired challenge seat, but changed so it can be removed using quick releases.