Mythbusters Bus Jump Small Scale

[diazona]

Sorry, I don't see where you're having a problem with it...

Out of curiosity I plugged some numbers into Mathematica and it reports that the curve $y(x) = -0.00121 x^2 + 0.0209 x$ satisfies the necessary conditions: $y(0) = 0$, $y'(0) = \tan(1.2^\circ)$, $y(50) = -2$ (all distances measured in feet). I don't know anything about highway construction, but that seems like a reasonable shape for a road.

 

[DaveC426913]

Sorry, I don't see where you're having a problem with it...

Out of curiosity I plugged some numbers into Mathematica and it reports that the curve $y(x) = -0.00121 x^2 + 0.0209 x$ satisfies the necessary conditions: $y(0) = 0$, $y'(0) = \tan(1.2^\circ)$, $y(50) = -2$ (all distances measured in feet). I don't know anything about highway construction, but that seems like a reasonable shape for a road.

Which looks like what? Can you post it?

 

[diazona]

Which looks like what? Can you post it?

OK, but I thought you would have been able to plot a function yourself :-/

It's not very steep. I know roads with much higher grades and which probably have greater curvature too.

 

[SystemTheory]

The image I recall from the Mythbusters show is a snap shot of the movie frame showing an LA style elevated highway with a section missing. Trying to estimate the actual geometry from such an image is difficult due to parallex error. The launch ramp would be 2 feet higher than the landing ramp (in DaveC sketch it is shown lower). The launch ramp would be at an incline of 1.2 degrees to the horizontal and the landing ramp at 0 degrees in my understanding. This could be a reasonable approximation for a missing section of elevated highway I suppose.

Edit: sketch attached.

 

[Integral]

2ft in 50ft is a 4% grade, but the ramp is angled up to have continuous road for some distance the grade would have to be greater then 4% isn't this pretty radical for a city bridge?

 

[SystemTheory]

Bus Jump Aerodynamics - Simplest Model

Simplifying Assumptions:

$\theta = 1.2$ degrees
$cos\theta = 0.99978$
$sin\theta = 0.02094$

Due to the large cosine and small sine most of the launch velocity directs into the horizontal component. To simplify the study of quadratic drag assume motion is purely horizontal.

Full scale bus jump variables:

M - mass.
A - frontal area.
C - drag coefficient.
$\rho$ - air density.
v - velocity in x-direction.

Drag Force:

$$D = \frac{1}{2}\rho CAv^{2}$$

Deceleration in Flight:

$$a = \frac{dv}{dt} = -\frac{D}{M} = -\frac{CA}{M} \frac{1}{2} \rho v^{2}$$

1/12 Scale Deceleration:

Frontal area at 1/12 scale is A/(12 x 12). Mass at 1/12 scale is M/(12 x 12 x 12). After substitution the factor 12 ends up in the numerator:

$$a = \frac{dv}{dt} = -12\frac{CA}{M} \frac{1}{2} \rho v^{2}$$

Comments:

These differential equations need to be solved for velocity as a function of time, and so far, there is no coupling with the increased vertical drop caused by deceleration. However one can see that the model bus is more sensitive to drag. The term (M/CA) is the ballistic coefficient in physics (the term is used differently for bullets). The final term 1/2 rho v-squared is the dynamic pressure. The full scale bus is 12 times more effective at pushing air than its scaled down model. The drag coefficient C is assumed to be the same for both cases.

 

[DaveC426913]

OK, but I thought you would have been able to plot a function yourself :-/
View attachment 22446
It's not very steep. I know roads with much higher grades and which probably have greater curvature too.

Hm. So the bus is leaving the ramp at almost horizontal and it has to fall less than 2 feet in the time it takes to cover a 50ft horizontal distance.

 

[SystemTheory]

I need to visit my calculations again. However it appears drag may have a negligible effect on the time to travel the jump distance on both scales. Using rough numbers I'm getting 1 millisecond at full scale and less than that at small scale. Next time I'll post a formula for time and horizontal distance for review.

 

[SystemTheory]

I'll post my draq equation if anyone's interested, but it appears the deceleration caused by drag can be neglected over the jump distance due to the bus having significant mass.

One factor that could cause the nose of the bus to drop is a torque impulse imparted as the front wheels of the bus catch air before the rear wheels. The weight W acting at the center of mass tends to impart a torque about the rear axle. This would be counteracted by a torque in the driveline, however, for a bus, the counteracting torque is probably insufficient. A motorcycle could provide more countertorque and the rider could adjust the center of mass rearward and use the throttle in mid air to help loft the front end.

An estimate could be made of the moment of inertia J and the the impulse torque, but at this point I lack good data so I don't plan any calculations.

 

[dr dodge]

I am glad to see someone else being "driven nuts" (pun intended) by mythbusters. their "myth-perceptions" on pressure drive me nuts
We give a basic pressure school at our facility, and myself and another instructor have threatened to send them a couple free passes
and they have even "myth-used" our products, too

ok, (breath deep) will not rant, will not rant

dr

 

[SystemTheory]

dr dodge,

I'd like to model some air cannons in an engineering simulator. Would your materials cover building the system model and writing the differential equations, or is it more basic stuff you offer?

 

[dr dodge]

System, I am a bit unsure exactly what you need. I have my own fab shop at the house. No mill or lathe (yet) but I know quite a few "job shop" guys around here. For my "day job" I deal in high accuracy high and low pressure metrology. ...but, at my house, for "personal R&D purposes" I can generate 40,000 psi (in less than 20 seconds) hydraulic pressure, and 15,000 psi gas pressure. I think we could very easily build some air cannon stuff.

I was originally going to post that I have found a "multitude" of used buses for under $2500... ranger probably knows a driver or two...
The ramp approach could easily be simulated in gravel
and we videotape it and start the new series
"engineering de-myth-defied"

dr

 

[SystemTheory]

I'm looking to do personal computer (silicon) simulations that explain and predict Mythbuster results with reasonable accuracy. This is engineering modeling problem with components such as fluid capacitor (air tank), fluid inertor (gun barrel), fluid resistor (heat transfer losses), ideal power transformer (pressure-volumetric flow power to force-velocity power), and mass of the projectile. I would "build and fire" this gun in a simulator on the computer but I don't have good data to compare to exit velocity from an actual air gun. Anyway I am not up for actual build and filming efforts as it is not along my interests or talents.

Does your company provide fluid power meters, which measure both pressure and volumetric flow rates? If so, please point me to a link or reference that helps with those measurements.

 

[diazona]

I finally got around to doing my usual writeup on this Mythbusters episode:
http://www.ellipsix.net/blog/post.80.html

 

[SystemTheory]

Great writeup. Thanks diazona. One thing I noticed in the episode was the short run to accelerate the model bus to 23 mph, and no clear reading on the radar gun. The radar gun could be off by +/- 1 mph according to some specs I've read. Also, once the front of the bus starts downward it is possible an aerodynamic downforce develops as well.

The takeoff drag force on the front of the full scale bus is > 1,000 lbs and on the scale bus at least 1/2 pound force (rough numbers). This doesn't slow the bus much over the short jump but I neglected the possibility of aero downforce.

 

[diazona]

Great writeup. Thanks diazona. One thing I noticed in the episode was the short run to accelerate the model bus to 23 mph, and no clear reading on the radar gun. The radar gun could be off by +/- 1 mph according to some specs I've read. Also, once the front of the bus starts downward it is possible an aerodynamic downforce develops as well.

The takeoff drag force on the front of the full scale bus is > 1,000 lbs and on the scale bus at least 1/2 pound force (rough numbers). This doesn't slow the bus much over the short jump but I neglected the possibility of aero downforce.

Yeah, well... if you do any quantitative analysis, post it here, I'd be interested to see if you can make the numbers work out. I actually considered running a simulation of the drag force on the bus, but what I wrote went on long enough as it was. What I'm aiming for is to give people* a taste of how physics applies in real situations, not to do a full accurate analysis.

*if anyone actually read my blog, which is doubtful ;-)

 

[dr dodge]

*if anyone actually read my blog, which is doubtful ;-)

i did
nice job

dr

 

[dr dodge]

system, pm'd the sensor info
(tried to refrain from shameless plug)

dr

 

[SystemTheory]

Tonight the Mythbusters tried to skip a sports car across 100 feet of water. The cars at 1/12 scale and full scale worked best with high velocity and no jump ramp.

The jump ramp caused cars at 1/1 and 1/12 to flip and land roughly nose first, what we used to call an "endo" when I raced motocross. One thing that contributes to the endo motion is the impulse imparted by compression and rebound of the rear spring at the lip of the launch ramp. I think this is what is causing the cars to rotate so much, and it may be a function of ramp angle and length being at the harmonic of the spring rebound. In other words the ramp length might need to be "tuned" to the suspension in addition to considering the weight, balance, and drive torque of the vehicle to get a machine to fly properly. If so some fairly complex physics are involved. In motocross the rider will preload the springs on a jump and use the rebound energy to best advantage. This video (maybe fake? looks real) has a car jumping a short fence successfully using a ramp a bit shorter than the length of the sedan.

http://clipaday.com/videos/redneck-car-jumping

 

[rcgldr]

Highways are not designed with launch ramp angles. The launch ramp and landing ramp point virtually right at each other.

Dave has the answer, perhaps it would be more simply stated that these aren't ramps, just 'level' sections of road with a gap in between. Imagine that the ramp was completed. No ramp would be designed to send a vehicle airborne for the distance covered by the gap in the movie, at least not at the speed the bus was going. The ramp sections are level, and given sufficient grip, a vehicle could probably take the completed version of ramp at 120 mph without going airborne. With the missing gap, the vehicle would start falling as soon as it entered the gap.

 

[SystemTheory]

Well, I have caught air on my motorcycle unexpectedly when crossing elevated train tracks at ordinary road speeds! But I agree a road should not have a 50 foot jump built in at 78 mph, so that part of the Myth/stunt is totally busted. In regard to getting a bus to jump 50 feet I watched the episode again last night. Grant says on the DVD release of the movie the out-takes describe (or show) the use of a pneumatic lift at the end of the launch ramp. I suspect it would impart an upward torque impulse on the front wheels to compensate for the downward torque impulse about the rear axle over the estimated time of flight.

 

[diazona]

i did
nice job

dr

cool, thanks Ideally I try to write something all the cool physics-y myths they do, but I've been missing a lot of them lately because of schoolwork. (Just got one up about "Unarmed and Unharmed" from last week, though, and sometime between now and this weekend I'll do the car skipping)