HELP! Curvilinear Motion

[ptc-2126605]

To All,

Please see the attached graphic to understand the curvilinear motion I would like to solve for using mathcad. Assume 600lbs body, all dimensions are in feet, velocity of 20 fts entering first drop. I am trying to estimate how far up hill the body will travel on a wet surface on its own inertia given the velovity described.

Thanks,

Ron

[Werner_E]

I cannot open the file using Prime 3.0.

You should have stated first hand which version you are using.

Above you wrote that you used Primes MCD converter. This means you have a full installation of Mathcad 15, so you could open it with that version.

BTW, the converter won't convert files with collapsed areas, so you have to open the worksheet in Mathcad 15, open the areas, save the sheet and then convert.

But to be on the safe side and because I recall that Alan isn't using Prime3, find attached the converted sheet as well as a pdf printout. The Prime file won't work because Prime does not support the data table alan used to get the data you provided in the sheet, so you will have to create the matrix XY in a different way (e.g. read in from the Excel file using READEXCEL).

Its very interesting to see the different appraoches of Fred and Alan but the big difference in the result between the two can't be not only just because Fred didn't consider the centripetal force, I guess.

[AlanStevens]

Ron Mickovitch wrote:

Hi Alan,

The graph looks interesting but I cannot open the file using Prime 3.0.

Thanks,

Ron

Sorry, I don't have Prime 3. As Werner says, you should have a copy of M15 with Prime 3. For this task and extensions to multiple body models M15 is almost certainly better anyway. (thanks for supplying the pdf copy Werner).

My model certainly needs to be checked carefully - I haven't even done that myself yet! I probably won't have time now to do this and examine Fred's model in detail for a couple of days.

Note that my model assumes the vehicle stays on the track; it becomes invalid the moment the Normal force drops to zero. I should really model both x and z motion and see how the trajectory matches the track profile. I think I'll look at this option next.

I've now done a couple of checks and I'm pretty sure my calculation of the radius is highly inaccurate (not surprising given that numerical differentiation tends to be noisy, and my calculation of radius depends on 1st and 2nd derivatives!). It would be helpful if you could specify the radii as a function of horiziontal distance (that is, give the radii and the distances where they change from one to another. Or supply the piecewise functional form of the surface profile.

Alan

[AlanStevens]

I've produced a modified version of my single-point model, with some checks - see attached for M15 worksheet and a pdf copy.

I'll now think about extending this to a multiple-point model to better represent an extended vehicle.

Alan

[ptc-2126605]

Hi Alan,

Thank you for moving forward on a solution.

Thanks,

Ron

[AlanStevens]

The attached files now contain an extended model in which the forces are calculated assuming the vehicle is spread out along the surface to its full length (the full length of the vehicle, that is). The dynamics still use a single point model. This is probably as complicated a model as is appropriate here (famous last words!), though more accurate specifications of the surface profile and its radii might lead to small changes in the results.

Alan

[ptc-2126605]

Hi Alan,

Could you grapgically provide an example what you are looking foer here "specify the radii as a function of horiziontal distance"?

Thanks,

Ron

[AlanStevens]

Ron Mickovitch wrote:

Hi Alan,

Could you grapgically provide an example what you are looking foer here "specify the radii as a function of horiziontal distance"?

Thanks,

Ron

On the very first diagram you provided you noted the radii of various sections (and lengths of straight sections). All I'm looking for is the same thing with the corresponding start and end x-values of each section.

Alan

[ptc-2126605]

Hi Alan,

Please see attachment. Let me know if this helps or if I have not provided the correct information.

thanks,

Ron

[AlanStevens]

Ron Mickovitch wrote:

Hi Alan,

Please see attachment. Let me know if this helps or if I have not provided the correct information.

thanks,

Ron

Ok, I hope I've interpreted it correctly. Attached is the extended model with these radii.

Alan

[ptc-2126605]

Hi Alan,

The final graph looks realistic. If I read it correctly this plot would suggest the sled would not make it over on its own inertia? I would like to apply this math to a known live case I have to see the relation. Is it just a matter of replacing the table in the "Basic Data" with a different case study?

thanks,

Ron

[AlanStevens]

Ron Mickovitch wrote:

... If I read it correctly this plot would suggest the sled would not make it over on its own inertia? ...

Correct. It depends strongly on other data though, like the initial velocity and the coefficient of friction. For example, if you reduce the coefficient of friction to 0.05 the vehicle goes much further - see image below for example.

.. I would like to apply this math to a known live case I have to see the relation. Is it just a matter of replacing the table in the "Basic Data" with a different case study?

Model validation. Excellent idea! You will need to alter all the relevant data as necessary. Profile (X-Z data), radii, mass and length of vehicle, coefficient of friction etc. You will probably need to alter the end time for the odesolve block and the initial guess for tau in finding the time the velocity reaches zero. If the validation vehicle reaches the end of the track there might be some other minor changes required (I didn't put a lot of thought into the end of the track as I could see the vehicle would get nowhere near it). I'd be very interested in seeing the results.

Alan

[ptc-2126605]

Hi Allan,

The results look great. If it is ok with you, I will be forward a new data set to run through. Your analysis is greatly appreciated.

Thanks,

Ron

[AlanStevens]

Ron Mickovitch wrote:

If it is ok with you, I will be forward a new data set to run through....

That's fine. I look forward to receiving it.

Alan

[ptc-2126605]

Hi Alan,

Working on the field data. Should have it early next week.

Thanks,

Ron