You don’t need the whole sphere to be flat, though, just the equator. I don’t have a deflated ball on hand to play with, but in my mind I imagine folding it into a bowl shape and then flattening the opening, so it’s like a piece of pita bread. There may be excess material in the “pole” region, but I think you could get the equator as flat as you please.
The ball will be in a bowl shape. That’s how the thick plastic walled balls are.It’s not like it’s a punching ball.
Diameter is any cord that intersects the center point of the circle.
Example of deflated ball. It’s not the best but it’s what I can find.
True, but when you deflate and flatten it your circle becomes an ellipse.
The length of an ellipse, even measured through it’s centerpoint, is greater than the diameter of a circle made with the same circumference.
Professional mathematican here. Just pointing that out because, well I’m appealing to my own authority, and I’m a topologist, which is pretty much the field of study that deals with stuff like flattened beach balls.
If you have a ball made of a totally non-stretchy material and you deflate it, the maxiumum possible length the deflated ball can have is one half the circumference. So if the ball is 9" long when deflated, the circumference (meaning the circumference of a great circle on the ball) will be 18" and the diameter will be a shade less than 6 inches, because the circumference is pi times the diameter.
Now in the real world, you probably didn’t squish the deflated ball in the exactly optimal way, but on the other hand you also have some stretch in your pilates ball material. These two factors will tend to cancel each other out. If you want to know how big your balls are going to be and the required precision is “within an inch or so” then your rule of thumb should be “the diameter of the inflated ball will be 2/3 the length of the deflated ball” or, working the other direction, “the length of a deflated ball will be one and a half times the diameter of the inflated ball.”
The balls described in the OP have deflated lengths of 6", 7.5" and 9" and will inflate to have diameters of 4", 5" and 6", respectively. All of these are smaller than the ball you currently own, which would be sold as a 15" ball.
If you need to measure your balls with greater precision than that, well, I suggest you reevaluate your priorities.
I measured the circumference of my inflated exercise ball last night and calculated the diameter to be 20.5 inches. Deflated, the length is about 29 inches. Tenebras’s 1.5 factor works out just about right. The deflated length probably would be an inch or two longer, but the thickness of the plastics prevents pulling the ends to a point.
You could also dip the balls into a liquid, preferably a tea, and measure the displacement.
Aren’t these things also color coded? So if you have a green 30", find the uninflated size of green and go from there.