The physics of maXair

For those who don't look at the front page, we've added a terrific article written by Dave "RideMan" Althoff about the physics of maXair.

http://pointbuzz.com/c/maxairphysics.aspx

And if you don't look at the front page on a regular basis, you're missing out on the latest news and updates!

*** Edited 3/19/2005 5:34:47 PM UTC by Walt***

Excellent article, even though im not sure i understood a lot of that... Keep up the good work Dave!

Whoosh! All right over my head. Very impressive, nonetheless.

Here's the bottom line, for those who just want to read the pictures...

Figure 1 shows what happens to you when the ride is not swinging, but the gondola is rotating. The red line is the outward force you feel because of the rotation, the blue line shows what gravity is doing, and the green line indicates what you feel.

In Figure 2, the ride is at maximum speed, as the gondola swings through the bottom-dead-center position. The scale of the force vectors is reduced here so that the drawing doesn't have to take up the whole page. The red line is still pulling out because of the rotation, the blue line is still pulling down because of gravity, but the purple line is also pulling down because of the swinging motion (rotation in another plane). That makes that green line...still what you feel...quite a bit longer. That's the 4.5G maximum force you feel during the ride.

In Figure 3, the ride is at maximum height. The gondola has reached the peak of the swing, so there is no force generated by swinging, rotation is still there (red line), and gravity is still there (blue line). So the green line pulls you up and back at about half of a G.

Force-wise, maXair does things that most coasters can't.

--Dave Althoff, Jr.

That makes more sense to me than having to look at all of those equations and going back and trying to figure out which parts of those are what. Still excellent!

That's really interesting cool. I find that stuff really interesting.

Wow you need to develop that and sell that to physics teachers. that is an outstanding set of lessons there that will allow physics teachers to combine so many good topics and show students the real life examples of things that physics controls

That's a very nice explaination of how the ride works. I've always thought that, reguardless of what aspect of it you're looking at, physics makes much more sense if you're applying it to a real life situation and not just staring at all those equations.

Nice work Dave. But what I would like to know is the amount of torque required just to get the ride started. I mean, with the weight of the arm and gondola, at a stand still, the moment of inertia has to be really high to get it moving.

RideMan,

I am not sure of your calculation for the g's in the normal component when the passenger is at the top, pendulum at 120 degrees. Gravity is acting downward and thus its component normal to the passenger is g*cos(120). The rotation of the gondola is 8rpm but this acceleration is towards the center of curvature of the gondola and thus does not add any to the normal component of acceleration. So the acceleration is -.5g's which is also what the manufacture Huss list on their technical information.

RideMan I always read and reread all your great articles just hoping to soak some of it up. ;) Please keep up the good work. I hope you know how much it is appreciated!

Beast Fan, it isn't 120 degrees, it's 135 degrees: remember, the seat is tilted back at 15 degrees. Also, the rotation doesn't add to the vertical component, but it will change the direction of the net force. Just because it isn't operating in the vertical plane doesn't mean you can simply ignore it. The main result of the rotation is to make the net force not go straight down; it offsets it a few degrees. Make sense?

--Dave Althoff, Jr.

Good article, Rideman.

I'm curious as to how much the ride will tend to twist the A-Frame supports when it's spinning at maximum rpm. Those support bearings at the top of the A-Frame must be dealing with more than just the pendulum motion of the ride - there's a gyroscopic moment there too.

Have you done any figuring of what the gyroscopic "forces" might be? I know the rpm are low, but the mass that's rotating is huge.

That's probably why the legs are on pivots at the base rather than hard bolted to the moorings.

(see http://www.cedarpoint.com/_upload/images/galleries/images/maXair023v.jpg)

That should allow for some give as the pendulum swings.

RideMan

I see what you are saying, but I was not ignoring it , but just looking at the vertical accelerations. The negative g's experienced by the rider is only going to be in the vertical direction. In this case the rotation is only going to accelerate the rider in the forward direction towards the restraint. The resultant acceleration is important to determine but does not yield the amount of negative g's at the top. That is the vertical componen which is just g*cos(angle).

I would like you to explain how you calculated your results with numbers and why Huss Sites List the min acceleration as -0.5g. I am also not sure if the seat is titled at 15 degrees. Is that an approximation that you made or did you get that from the manufacture.

thanks

The rotation is going to pull outward in the plane of rotation. The rider is tipped backward fifteen degrees (that number comes from Huss) and therefore the plane of rotation is 'down' fifteen degrees, which is why the rotation has an effect on the vertical force.

Based on the huge experience of HUSS with seating systems, the GIANT FRISBEE seats are tilted backwards 15°, bringing the resulting acceleration exactly into the line of the spinal column. Therefore, the forward push into the restraint is minimized, ensuring a nice and comfortable ride.
(H. Berkelmann, "The Secret of Superior Power")

The thing is, the point at which you get that -0.6G is a special case. Only one seat is going to have that force, and that only instantaneously because everything is moving. My suspicion is that the number Huss supplies (-0.5G) is based on the center of the gondola, where there are no seats, or at the very least does not take the seat angle into account. It's not that they are wrong, it's just that they did their measurement in a different way. :) Notice that the numbers I came up with are actually lower than what Huss publishes, so their figures, while arguably less precise for the special case of the seat I picked, are reasonable. You get -0.5G. If you are lucky, you might get slightly less. To put it into perspective, 0.13G is equivalent to 4.16 ft/sec/sec, which will take you 0-60 in about 22 seconds. We're not talking about a huge variation here, particularly compared with the total force variation on the ride.

Somewhere I have the notes I used to work out the forces trigonometrically...my math skills are so poor and my calculus so rusty I tend to do things the hard way. :)

--Dave Althoff, Jr.

Hi,

I can't reach the article. Could you please help me to reach article.

Thanks.

It's available here:

http://pointbuzz.com/c/maxairphysics.aspx

Walt,

Thank you very much.