Acceleration Details

Fairly accurate calculations on Dragster's acceleration:

It is difficult to measure with precision the exact duration of Dragster's acceleration.

However, it is a fairly simple matter to measure the distance it takes to reach its terminal velocity of 120 MPH (176 fps). This distance from the start to the end of Dragster's acceleration is approximately 300 feet +/- 4 feet or so. That's the distance from the start position to approximately the south edge of the entrance tunnel. (At this point, the sled begins is rapid deceleration to zero, and the train has reached its terminal velocity.)

Knowing the final velocity, and the distance it takes to reach that velocity allows us to calculate the time it takes to go that distance, and from that, the acceleration.

The distance d = 0.5vt, where v = 176 fps and d = 300 ft. Rearranging we have t = 2d/v = 2(300)/176 = 3.409 seconds.

The acceleration a = v/t = 176 fps/3.409 seconds = 51.63 fps/s = 1.61 g's.

From this, we can calculate the speed and position at any point along the course.

t in sec_____v mph______v fps________d ft

___1_______35.20______51.63_______25.81
___2_______70.40______103.25_____103.25
___3______105.60______154.88_____232.32
_3.41_____120.03______176.05_____300.16

Also, the distance from the start position to the first camera is approximately 192 ft. The train traverses this distance in 2.72 seconds, at which time the train is going 140.8 fps, or 96 mph. *** Edited 6/15/2004 2:13:26 PM UTC by Mach1***

Whoa, my brain hurts. That's some pretty cool stuff though!

someone bored at work today???

John

Wow! And I thought there would be no use for math after school. :)

The only problem with that is that it assumes continuous acceleration. I don't know for certain, but I think that if you were to look at a chart of the ride's acceleration, you would find that the acceleration is not continuous for the length of the launch. Also, the exact point at which the acceleration ends will vary slightly with the mass of the train, as when the launch reaches top speed, the drive motor is immediately shut down and the train quickly over-runs the launch sled.

Hmmm... I wonder if I have any video that shows the whole launch from far enough away to do some analysis to a resolution of 1/29.97 second...

--Dave Althoff, Jr.

Yeah you can feel it kind of speed up right around halfway.

Awsome. I love math and physics!

I think RideMan has a good point. Not knowing the exact working of the launch system, I'd think that the acceleration would taper off. You've got compressed Nitrogen expanding, which drives the hydraulic fluid, which drives the cable rotor. From what I've learned, the expansion of the Nitrogen (or most gases for that matter) won't be completely uniform. As you near the end of the expansion, the force it's applying to the hydraulic fluid decreases. Not a significant decrease, but enough to make the acceleration non-uniform.

Also, you could look at the mass of the train having an effect. Wouldn't a lighter train accelerate faster initially? It accelerates faster, hits top speed earlier, so the motor shuts down earlier. There's been some discussion here about how the early shutdown works. I don't recall if it was based on the measured speed of the train via sensors, or the rpm of the cable drum?

Mach1, how did you go about measuring the launch length? Did you pace it out?

Also, there was an interesting series of articles written for Rollercoaster! magazine about coaster dynamics. Some of the math can get a little ugly in there, but they're interesting regardless.
http://www.me.rochester.edu/~clark/coast.html *** Edited 6/15/2004 8:57:16 PM UTC by Montu***

The length of the launch run was calculated on this based on the assumption that the fence posts are 8 feet apart. This may seem a great leap of faith, but most construction is done in standard engineering units; 16", 4', 8', 12', etc.

From there its a matter of counting posts. From the start position to the first camera is 24 posts = 192'. From the start position to the south end of the entrance tunnel is 38 posts = 304'. (Comparing scaled aerial photos and web cam shots bear these out to be fairly accurate.) The acceleration ends approximately just south of the entrance tunnel, say 300' from launch. This is based on observation of several trains while positioned near the hydraulic building, and listening to the cable during launch. From listening, the cable appears to accelerate at a fairly uniform rate.

I realize that there is some variance from launch to launch, and that my measurements are approximate, but these values are in the ballpark. :)

I kinda expect posts like this when there is 4ft of snow outside my window.

Suspenders to tight today? Seems like all of your blood has rushed to your brain with that much detailed information! ;)

I hear ya, Dan. Although it has been pretty crappy out the past few days... I still enjoy these threads, anyways.

What do you want us to do about it?

For starters, you can contribute something worthwhile to the forum and stop being an idiot.

Funny thing is I did the same calculations when I was waiting in line for TTD when the last season opened. I'm calculating what miles per hour is in feet per second. Since TTD motto is 120 in 4 seconds I used those numbers and calculated about 1.5 horzontal Gs. I decided against getting down on the ground and calculating up what the total acceleration was.

but the only thing that is wrong with that is that you are declining the fact that the train launches at a lower height that when the sled lets go. So the train is going up hill not straigt

Yeah that's a really good point. Then you have to find out much higher it is at the end and do some a^2 + b^2 = c^2

Well, I'm standing in line at TTD at the early Joe Cool Club time, I'm not interested in calculating Pythagorean theorum lengths.

I understand what Rideman means with the system shutsdown after it reaches 120mph but wouldn't that mean the train starts to lose speed once the launch phase stops. This would have to do with why empty trains rollback a lot more than full trains. If you think about it if the train start the acent up the tower at 115mph or it starts at 119mph that's a 4mph difference at the top. To me it sounds like a bad way of doing things.

Why wouldn't Intamin have the ride weigh the trains mass and launch it at the rate it where it would always be going 120mph at the very end of the launch.

Too much additional costs probably. It would also probably take a while for the calculations to process also.