Hi.

A 2 metre long solar panel has its frame supported with a post(s) into soil. The lower end is held anchored to flat soil. What is an optimal position "?" to get less convex bending or concave sagging ? Its ~20Kg weight distribution is very uniform, there is nothing more massive at any place.

Does this help?
https://en.wikipedia.org/wiki/Airy_points

9 hours ago, Externet said:

Hi.

A 2 metre long solar panel has its frame supported with a post(s) into soil. The lower end is held anchored to flat soil. What is an optimal position "?" to get less convex bending or concave sagging ? Its ~20Kg weight distribution is very uniform, there is nothing more massive at any place.

There is not enough information about your proposal to properly comment.

Surely the panel frame provides the support and specifies mounting methods ?

I think what you might need for an array would be what roofers call an underpurlin.

Certainly you would need to support the frame edges at these points,

John's idea, though interesting, is not really suitable as these supports are designed to be as near as possible the same horizontal level, quite unlike yours.

Better information will get you a better answer.

Edited May 27May 27 by studiot

Thanks, gentlemen. These use a single support post and the lower edge to soil :

These show 2 extra sloped support elements as rafters under each 'column' of panels, as to not attach to the panel frame. The intention is to use the panel frames as rafters for single rows of panels, not as four+ high as in the left image. At the right side image, the optimal location of the single post by the person left knee is dependent of the length of the panel to be supported.

Simple kits are :

Where I see the sloped element being redundant to the panel frame, and the horizontal one, not needed.

No underpurlin; instead the location of the post in function of a given panel length.

This image below has front post, rear post and rafter under the underpurlins Trying to get rid of too many elements.

A trawl round the net shows various support frames, nearly all have underpurlins, including your pictures.
I did find some glorified deck chairs and some interesting sloping plasic tubs weighted with bags of earth or stone.

These latter raise an interesting point as you seem to be thinking of buying only panels and assembling your own support.

Have you considered climate conditions ?

The panels are like sails or fence panels and are subject to significant variable wind forces.
The variability means that the ground reactions are contantly being worked back and fore, which is how fences blow over as the posts works loose in the ground.
This will also continually flex the panels themselves.

A final thought.

Panels are rated for 20 - 25 years life, but I wonder what suppliers / manufacturers would say about the guarantee if they are not mounted on the recommended supports.

In the UK many suppliers resort to the " Not installed in accordance with recommendations/instructions." to wriggle out of early failure.

For a 2-meter solar panel with uniform weight distribution, the optimal support position would be approximately at the center of gravity - around 1 meter from either end. Here's the reasoning: Structural Analysis: - Placing the post at the midpoint (1m mark) minimizes both sagging and bending moments - This creates equal cantilever lengths on both sides - The lower end anchored to soil provides additional stability However, practical considerations: - If wind load is significant, moving the post slightly toward the raised end (maybe 1.1-1.2m from bottom) can help - This reduces the moment arm for wind forces - The anchored lower end already provides good resistance For a 20kg uniform load, centering the support at 1m from the bottom end would give you the most balanced distribution and least deflection overall.

41 minutes ago, M Tanzeel said:

For a 2-meter solar panel with uniform weight distribution, the optimal support position would be approximately at the center of gravity - around 1 meter from either end. Here's the reasoning: Structural Analysis: - Placing the post at the midpoint (1m mark) minimizes both sagging and bending moments - This creates equal cantilever lengths on both sides - The lower end anchored to soil provides additional stability However, practical considerations: - If wind load is significant, moving the post slightly toward the raised end (maybe 1.1-1.2m from bottom) can help - This reduces the moment arm for wind forces - The anchored lower end already provides good resistance For a 20kg uniform load, centering the support at 1m from the bottom end would give you the most balanced distribution and least deflection overall.

Why only one support ?

The OP had at least 2

42 minutes ago, M Tanzeel said:

minimizes both sagging and bending moments

I'm sorry what's the difference ?

4 hours ago, M Tanzeel said:

For a 2-meter solar panel with uniform weight distribution, the optimal support position would be approximately at the center of gravity ...

... (maybe 1.1-1.2m from bottom) can help - ...

The intention was not to find "approximately" nor "maybe" , but a mathematical point where a panel (or beam) will have the least convex bending or concave sagging, being one of the two support points its lower edge when wind is from either side or deformation by only its own weight.

If it was horizontal, its depiction would be :

But it is not ☹️.

As it is not horizontal and angle varies with installation and latitude; let's set to 45 degrees if that was the absent '-not enough information-'.

Edited November 10Nov 10 by Externet

The sag left to right will be bigger than the sag from top to bottom anyway, because it's a longer unsupported span.
If it matters, you should address that first.

14 hours ago, Externet said:

The intention was not to find "approximately" nor "maybe" , but a mathematical point where a panel (or beam) will have the least convex bending or concave sagging, being one of the two support points its lower edge when wind is from either side or deformation by only its own weight.

If it was horizontal, its depiction would be :

But it is not ☹️.

As it is not horizontal and angle varies with installation and latitude; let's set to 45 degrees if that was the absent '-not enough information-'.

This diagram shows entirely unsuitable support conditions at both supports.

A good deal more information is required before a more accurate structural analysis can be performed.

You didn't respond to my last answer to yourself either, back in May.