I love to swing on tall playground swingsets and just about any swingset in general. I am 22 years old.
I was wondering if a smaller swingset induces more G forces that a larger and taller one? I have read that swingsets can put 1.5 to 2 gs on your body when you are at the lowest part of your arc.
Will I pull more G forces on my 13 foot heavy duty commercial grade swingset in my backyard when I do full height swinging, than full height swinging on a 8 foot tall swingset? Does the height of the bar and the size of the arc make a difference in the maximum g forces pulled? I should ideally be achieving a greater max velocity when at the bottom, on my 13 foot tall swingset that a 8 foot tall one.
What could be my max speed in MPH at the bottom of my arc when full height swinging?
The further you are away from the swing’s fulcrum, the more acceleration you can accrue in your decent, and the more Gs this should enforce. Though I’m sure there are limiting factors, I think that yes, you should feel more Gs on your 13’ swingset.
No, the “gee force” only depends on the size of your swinging arc, not on the height of the top bar.
For tiny arcs (say, 1 degree forward and 1 degree back), you’d experience barely more than 1 gee. For a maximum arc of 90 degrees forward and 90 degrees back, you experience 3 gees at the bottom of the swing. Moderate arcs in between these extreme examples will give the more typical 1.5 - 2.0 gees you read about. This calculation is the same regardless of the height of the top bar or the distance from the seat it’s connected to.
However, your maximum speed IS affected by the distance from the seat to the top bar. You said your top bar is 13 ft off the ground (3.9624 meters), but you didn’t specify how low the seat is. I’ll assume the seat is 0.9624 m off the ground, so the distance is exactly 3 meters. You said “full height swinging” but you didn’t specify what that means. I’ll assume you meant 60 degrees forward and 60 degrees back, so at the top of your swinging motion your mass is 1.5 feet higher off the ground than it is at the bottom. That’s h.
Your potential energy is mgh. At the bottom of your swing, all of this is converted into kinetic energy, (1/2)mv^2. So mgh=(1/2)mv^2 hence v^2=2gh. In this case, h is 1.5 meters (and g=9.80 m/s^2) so v is approximately 5.42 meters per second, (which is about 12.1 miles per hour).
On an 8 foot swingset, let’s say h=.75 m, so your speed is reduced by a factor of sqrt(1/2) to 3.83 m/s.
As for the gee forces, there the weight your normally feel just sitting there (1 gee) and then on top of that you have the actual acceleration of the swing trying to pull you into a circular motion instead of moving straight ahead by Newton’s 1st law of motion. That force is pulling your towards the center, so it’s centripetal force, which is given by F=mv^2/L (where L is the distance from the top bar to the seat, which is not the same as h which is the difference in height between the top of your arc and the bottom of your arc). We already know v^2 = 2gh, so we can substitute that in and we have F = m(2gh)/L. If your arc is 90 degrees, then h=L and we get F=2mg, hence you are accelerating upwards at 2 gees, plus your actual weight of 1 gee, makes you feel 3 gees. But if your arc is 60 degrees, then h=.5L hence F=mg and you’re accelerating upwards at 1 gee, plus your actual weight of 1 gee, makes you feel 2 gees.
For any arc A, h=sin(A)*L, and then the gee force you feel is 1+2sin(A). This has nothing to do with the height of the top bar, only the size of the arc.
In that case, you get 3 gees at the bottom of your arc, regardless of the height of the top bar.
And your maximum speed is sqrt(2gh) where h is the difference in height (in meters) between the top of your arc and the bottom of your arc and g is 9.80 m/s^2 . That gives you an answer in meters per second. If you want statute miles per hour, multiply by 2.24.
If the top of your arc is 3 meters higher than the bottom (roughly 10 feet) then your maximum speed is sqrt(29.803) = sqrt(58.8) = 7.668 m/s then multiply that by 2.24 and you get 17.2 mph.
The force would be the same as if you hit them traveling at 17.2 MPH. What force that would actually be would depend on how soft you and your target are, how easily they move, and so on, but I suspect that force isn’t actually what you’re interested in knowing.
Oh, also, all calculations so far have assumed that you’re a point mass at the end of the near-weightless chains. The approximation that the chains are weightless is probably pretty good for a real swingset, but the point mass approximation probably isn’t. In reality, your mass will be distributed and some of it will be significantly closer to the center, which will decrease the speed.
What is the best way to raise my 13 foot tall 370lb swingset upright and into pre-dug footer holes?
Using a pickup truck to pull on some ropes attached to the 3 1/2 inch top pipe to raise the swingset up to a standing position?
Or using a back-end loader to raise up the top pipe of the swingset with the top bar in the bucket? So the swingset is dangling from its top pipe and being lowered into footer holes?.
Height off the ground doesn’t matter. What matters is the difference in height between the top of the arc and the bottom of the arc. That gives you potential energy which can be translated into kinetic energy.
But increasing the potential energy still won’t affect the gee forces. Larger swingset means more energy but it also means a gentler curve. Smaller swingset means less energy but with a tighter curve. The gee forces are the same for small swingsets and large ones, 1+2sin(A) where A is the angle of how you swing. The OP specified 90 degrees, to that’s 3 gees at the bottom of the arc.
Okay, I think I became confused with sbunny8’s wording, thinking he/she was saying the height of the swingset (and therefore the distance from the pivot on the bar and your seat) didn’t matter when it came to how many Gs you pulled.
I was assuming the length of the chains would grow proportional to the height of any arbitrary swing set, but I think he was not necessarily making that assumption, and you could have a 13’ and 8’ swing set with the same chain length on the swing.
So am I correct in thinking the longer the chains (from pivot to seat) the more Gs you can pull?
Right, understood now on that point (I think!). Thanks.
So, extrapolating this into a ridiculous scenario, if I were on a swing with a 100 foot chain, would the acceleration of gravity from such a greater height bring more force into the equation, or is it equalized out buy a much longer arc?
I tried a bigger arc swing the other day. You quickly reach a maximum speed, trying to go faster just results in slowing down faster… (aerodynamics are like that…) and its hard work to get a little faster .