# How to calculate how strong is seat post?

Is 27.2mm seat post stronger than 25.4mm because it has bigger diameter?

How to mathematically calculate how much 27.2mm stronger than 25.4mm provided both seat posts have same length, wall thickness and made of same metal?

If i have to use 25.4mm seat post how i calculate ideal wall thickness i need so it be as strong as 27.2mm? for instance 25.4 with 1.5mm thick walls is same strong as 27.2mm with 1mm thick walls? Is there formula to calculate exactly?

• Really this belongs on an engineering web site. Bicycle seat posts under normal riding do not need to be particularly strong, they need to be build much stronger to handle accidents and miss handling (e.g. seat hitting ground when bike falls over) Jun 2, 2022 at 21:58
• @mattnz I think it's fair game... the relationship between diameter, wall thickness, stiffness, and strength comes up in a lot of places on bikes and is helpful to understand Jun 3, 2022 at 4:24
• @NathanKnutson I agree. Perhaps the question could be generalized, with this situation being used as an example. Jun 3, 2022 at 4:29

My understanding is that as the diameter of a hollow tube increases, the strength increases by the fourth power.

The elastic section modulus equation for a pipe r2 is external radius, r1 is internal radius (d2, d1 being ext diameter and int dia respectively.)

Outer Diameter Wall thickness "Area Moment Of Inertia" Required wall
25.4mm 1.0mm 5,714 Target
25.4mm 1.5mm 8,073
27.2mm 1.0mm 7,072 0.79mm
27.2mm 1.5mm 10,032
31.6mm 1.0mm 11,263 0.49mm
31.6mm 1.5mm 16,103

So if you went from a classic 80's seatpost of 1" across, with a 1mm wall thickness, then a 31.6mm seatpost could be half the thickness to be the same strength.

On the downside, the weight has gone up by some small amount, as has the cross-sectional area resulting in a less-aerodynamic shape.

These values do not take into account the total length of the seatpost, nor its supported and unsupported lengths.

• People who know maths better than me are welcome to pick holes in the above. I've pieced it together from several sources, and doubtless has errors.
– Criggie
Jun 3, 2022 at 10:05
• The second moment of area of a solid round bar is indeed proportional to fourth power. However, you have to understand that stress at the side is inversely proportional to second moment of area, but proportional to distance from centerline. So the side of the round bar has stress inversely proportional to third power. Also the weight is proportional to second power, so the stress-weight-product is inversely proportional to only the first power of radius. The same is true for tubes: stress is inversely proportional to weight and first power of radius. Same weight, 2x radius, means 2x strength Jun 3, 2022 at 15:50
• Also we can arrive at the same with dimensional analysis. The load of interest in the tube is bending moment, which is measured with Newton-meters. Maximum stress a material can withstand is measured in Pascals or Netwons per square meter. To arrive at Newtons per square meter from Newton-meters, you need to divide by the third power of dimension. Not the fourth power of dimension. Jun 3, 2022 at 16:11
• ...also if you fix the wall thickness to a certain value, you have already "used up" one power of dimension, so you're left with two powers of dimension. Hence with equal wall thickness but different diameter, the strength is inversely proportional to second power of diameter. Jun 3, 2022 at 16:12

Is 27.2mm seat post stronger than 25.4mm because it has bigger diameter?

Yes.

How to mathematically calculate how much 27.2mm stronger than 25.4mm provided both seat posts have same length, wall thickness and made of same metal?

Firstly, a 27.2mm seatpost is heavier than a 25.4mm seatpost having the same wall thickness. Specifically, it has 1.0709x times the weight. This fact that there's more material strongly suggests (but does not prove) that it's stronger.

A beam with a certain bending moment M (defined as force times the lever arm at which the force acts), radius r and second moment of area I has the maximum stress:

``````sigma = M*r/I
``````

So we need to know the second moment of area.

For a tube, it is

``````I = pi/4 * (r_2^4 - r_1^4) = pi/4 * (r_2 - r_1) * (r_2^3 + r_2^2*r_1 + r_2*r_1^2 + r_1^3)
= (approximately) pi*(r_2 - r_1)*r^3
``````

Here `r_2 - r_1` is the wall thickness and `r` is the approximate radius (inner or outer, doesn't matter, as they differ only very little from each other).

So the maximum stress is:

``````sigma = M/(pi*(r_2 - r_1)*r^2)
``````

Here everything else is constant but `r` differs. It is 1.0709 times bigger in the bigger seatpost. So the bigger seatpost has `1/1.0709^2 = 0.872` times the stress. It's about 15% stronger.

However, the bigger seatpost is also 7% heavier. Nevertheless, because the strength differs more than its weight, it is still stronger per unit weight.

If i have to use 25.4mm seat post how i calculate ideal wall thickness i need so it be as strong as 27.2mm? for instance 25.4 with 1.5mm thick walls is same strong as 27.2mm with 1mm thick walls? Is there formula to calculate exactly?

With same wall thickness the larger seatpost is `(27.2/25.4)^2` times stronger. So you need `(27.2/25.4)^2 = 1.1468 = (approximately) 1.15` times thicker walls to make it of equal strength.