Which Umbrella Base is Best for Windy Conditions?

Which Umbrella base is the least likely to tip over, Round base, Triangle Base or Square base ?
Trying to work out which is the best Umbrella base to have in the garden on a timber deck , Round base, Triangle Base or Square base ?
I have noticed my round base Umbrella at home tips quite easy at home and at work I have noticed some umbrellas in strong wind stay standing.

The weights and shape of Umbrellas are various but overall , if all umbrellas where equal height weight and shape, Which base wins ?

Could someone help me not so much with the mathematical equations but the conclusion of : If a wind blows in an increasingly east direction 25km or more on an open umbrella with a square base or a triangle base or a round base. which umbrella will stay upright longest ?

The one with the edge at the greatest distance from the umbrella pole, in the direction of the wind.

The principle of a lever applies, the only difference being that one end is 90° from the other.

Assuming that the torque from the wind and the weight of the umbrella is the same, then what matters is the width of the base (in the direction of the wind, for a specific case).

Otherwise - just nail it down

Welcome to PF.
Assuming the bases have the same mass and area.
1. The round base will be best.
2. The square base is next.
3. The triangular base will tip first.

Umbrella curious said:

... I have noticed my round base Umbrella at home tips quite easy at home and at work I have noticed some umbrellas in strong wind stay standing.

Welcome!

Is it possible that the bases of those umbrellas at work are much heavier than yours at home?
Could those be even anchored down to the floor?

Perhaps those at work are shielded from strong horizontal airflow and gusts due to proximity to tall buildings or trees?

Lnewqban said:

Is it possible that the bases of those umbrellas at work are much heavier than yours at home?

The height of the pole will be relevant, also the area and actual shape of the curve of the canopy. And one last thing; the flexibility of the pole can make a difference- both to the change in the cross-sectional area and and in any resonance frequency vs the wind gusts.

Just use a very heavy circular base and stop worrying.

If the wind direction is unspecified or variable, then orientation of the base is not important.

Identify the polygon that forms the convex hull of the base outline.
On a solid surface, the base will tilt about one edge of that polygon.
https://en.wikipedia.org/wiki/Convex_hull

Identify the centre of total base and umbrella mass on the ground.
Identify the radius from the centre of mass to the closest edge.
Stability is proportional to that radius.

For the same total mass, if the base area is 1.00
A circle has a stability of; 1/√π = 0.564
A square has a stability of; 0.500
An equilateral triangle has a stability of; 0.439

I had a back deck on a single-story house that overlooked Penobscot Bay in Maine. The round deck table had a central hole that supported an umbrella whose top was nearly continuous with the line of the hiouse roof. in altitude We had a pretty good steady onshore wind (maybe 40 knot) one afternoon and the airflow over the umbrella lifted it straight up out of the table and it flew entirely up and over the house Mary Poppins-style and landed in the front yard. So beware the aerodynamics lift as well as the drag.
Nice house.