Tripod Physics

TL;DR

To prevent a tripod from toppling over by wind, it is better to attach the weight at the end of each leg than to hang a sandbag on the hook.

Tripod stability

I usually use a tripod as a light stand at an outdoor shooting (*1). The wind is my biggest enemy because it knocks down the tripod as soon as I attach a light diffuser (like an umbrella) to the flash. What I didn't understand was why the tripod seems to topple over no matter how much weight I add to the sandbag.

The hook for the sandbag is usually on the tripod's center column. I thought attaching the weight at the end of each leg would lower the center of gravity and make it more stable.

In the pictures below, I'm pulling the top of the tripod to the right (as the wind would do) with a luggage weight scale. [Left] has three water bottles hanging on the center column. In [Right], I attached one bottle to the end of each leg using hook and loop, how much more force does it take in [Right]?

The answer may surprise you ;)

If you want to feel "OMG! I used to be able to do math in highschool!" like I did, please give it a try yourself (see Appendix below).

Then I realized the difference is in the work required for the wind to tilt the tripod up to the tipping point. As you can see the tripod can tilt much more in [Right] before it starts to topple. So the solution is to attach a weight to the end of each leg using a tape or hook and loop. You can use wrist weights, canopy weights, etc. as well.

When doing that, you have to make sure the tripod stays open when it is tilted. The tripds with struts like this are fine. Otherwise you have to add your own struts. (In the pictures above, you see my white 3D-printed spacer that is keeping the tripod open.)

My ultimate solution was to use rebar with hook and loops at each end. They are heavy but they fit in my tripod bag. With those rebars attached, my tripod never even tilted during a shoot at the very windy beach :)
(*2)

Notes: (*1) Regular light stand cannot be used on an uneven terrain. C-stands are heavier and only folds into a big "L" shape which won't fit into my tripod bag.

Appendix

Tripod Physics Question

These two figures show a tripod with length L and height H seen from the top and side, respectively. Assume the tripod is completely rigid and has no weight (wow!) and the wind force is applied to the top trying to topple the tripod to the right.

(1) Case [A]: When the weight W is attached to the top, what is the wind force needed to lift the leg on the left off the ground? How does it change for case [B] where one third of the weight (W/3) is attached to the bottom of each leg?

(2) What is the amount of work needed to tilt the tripod up to the tipping point for Case [A] and Case [B]?

Experiments

In my real-life case, the weight of the tripod itself is 1.8 kg; three bottles are 1.4 kg all together; three rebars are 6 kg in total.
Spoiler Alert:
The weight scale showed 0.25 kg to lift one leg when there is no weight, 0.6 kg when 3 bottles on center column, 0.6 kg with one bottle on each leg, and 1.55 kg with 3 rebars.