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

[AlanStevens]

If "wet surface" means no friction, then, assuming no drag also, the initial kinetic energy can be equated to a gravitational potential energy through (1/2)v^2 = g.deltah. Given an initial velocity of 20ft/s this gives a delta h of about 6.2ft., so the cart would keep going forward until it came to a hill that was higher than 6.2ft more than the height of the starting hill. However, to do this more precisely, with drag and friction, we'd need to know more (drag coefficient, cross-sectional area, rolling friction correlation etc.)

Alan

[dschenken]

All people need to know about physics when applied to mechanics:

http://xkcd.com/669/ Experiment

[ptc-2126605]

Hi Alan,

I am extremely appreciative of you reviewing my request for a Mathcad solution. To answer your questions. Please use a friction of 0.08 and assume no drag. To be more descriptive the vehicle is about twelve feet long on a smooth resin surface with an average weight of 600lbs. Look forward to any help you can provide.

Thanks,

Ron

[ptc-2126605]

Additional information:

Vehicle width: 46"

[AlanStevens]

I started to look at this in more detail, but I'm a little puzzled (not unusual!). Does a straight section meet a curved section at a tangent to the curved section or not? I assumed it would, but then the heights don't seem to match your picture (I could have calculated them incorrectly of course!). Also, is the vehicle really 12 ft long? This seems very long in comparison to some of the section lengths. Does it have wheels front and back, or is it a flat surface in contact with the surface?

Alan

[ptc-2126605]

Hi Alan,

Yes the straights do meet the curved section at a tangent. I will prepare a better detailed drawing for you. In particular describing the radius's. The heights may be fooling you because there may be mor than one radius in a curve. Sorry about that. I thought it would be easier to average them out. The vehicle is actuall 11' 6" long. It is a flat inner tube, no wheels and it is in contact with the surface. I am sorry I am being a bit illusive for proprietary design reasons. Do you use any cad programs such as Autocad that I could provide a drawing to you? I really appreciate your help on this.

Thanks,

Ron

[AlanStevens]

Hi Ron,

Aah! A flexible cart - I'd been thinking rigidly (pun intended!). I'm afraid I don't have Autocad (nor any other Cad software).

Alan

[VladimirN]

Alan,

You can use free Creo View Express to view ".dxf" and ".dwg" files (and many other CAD file formats):

http://www.ptc.com/products/creo/view/express/

32-bit (91 MB): http://www.ptc.com/WCMS/files/128970/en/CreoView_Express_32.exe

64-bit (98 MB): http://www.ptc.com/WCMS/files/129038/en/CreoView_Express_32_64.exe

P.S. Or free "DWG TrueView" from Autodesk for viewing ".dwg" files available here:

http://usa.autodesk.com/adsk/servlet/pc/index?id=6703438&siteID=123112

http://download.autodesk.com/esd/dwgtrueview/2014/SetupDWGTrueView2014_ENU_32bit.sfx.exe

[AlanStevens]

VladimirN. wrote:

Alan,

You can use free Creo View Express to view ".dxf" and ".dwg" files (and many other CAD file formats):

http://www.ptc.com/products/creo/view/express/

32-bit (91 MB): http://www.ptc.com/WCMS/files/128970/en/CreoView_Express_32.exe

64-bit (98 MB): http://www.ptc.com/WCMS/files/129038/en/CreoView_Express_32_64.exe

P.S. Or free "DWG TrueView" from Autodesk for viewing ".dwg" files available here:

http://usa.autodesk.com/adsk/servlet/pc/index?id=6703438&siteID=123112

http://download.autodesk.com/esd/dwgtrueview/2014/SetupDWGTrueView2014_ENU_32bit.sfx.exe

Thanks for this Vladimir.

Alan

[ptc-2126605]

Hi Alan,

I am back again from the holidays. I really appreciate your interest in helping me out up to now. I realize I have not provided enough information for you to continue. Please let me know what I am missing. I believe we left off where heights were not making logical sense. I can prepare a more detailed drawing. Looking forward to your comments.

Thanks,

Ron

[Fred_Kohlhepp]

Rather than your (very pretty but incorrect) picture, a table of X vs Y points that would allow a spline fit to your "hills" would be a great place to start.

[ptc-2126605]

What should the X spacing be ?

Thanks,

Ron

[Fred_Kohlhepp]

Something convenient, a foot(?)

[AlanStevens]

Fred Kohlhepp wrote:

Something convenient, a foot(?)

The x-spacings don't have to be regular, but there should be enough x-y pairs to provide a reasonable definition of the shape.

Alan.

[ptc-2126605]

Hi All,

I have attached a spreadsheet of the XYZ coordinates for the spline. Let me know if you have any questions.

thanks,

Ron

[ptc-2126605]

PDF of Points Plan and Profile.

[AlanStevens]

Ron Mickovitch wrote:

Hi All,

I have attached a spreadsheet of the XYZ coordinates for the spline. Let me know if you have any questions.

thanks,

Ron

I assume the units are feet. This is what the profile looks like in Mathcad. The peaks are slightly flatter than your pdf profile.

I'll assume this is ok unless you say otherwise.

Alan

[ptc-2126605]

Hi Alan,

Looks good. Yes the units are feet. The vehicle (inner Tube) travels from right to left on a wet surface entering the profile at 20 fts.

[Fred_Kohlhepp]

Right to left?

First pdf picture implied left to right!

[ptc-2126605]

Hi Fred,

Yes direction has changed as the profile is now mirroed. I appoligise for that. I can rebuild the coordinates back to the original travel direction to match the first PDF?

Thanks,

Ron

[Fred_Kohlhepp]

Not a problem, just clarifying.

[ptc-2126605]

Profile looks great! As Fred noticed the direction of travel is now Right to Left.

[AlanStevens]

Good job Fred is on the ball - I wouldn't have noticed!

Alan

[Fred_Kohlhepp]

Well, if I did it right, you'll go whaling off thhe end at about 10 ft/sec.

[Werner_E]

Well done!

But I think you should define slp(x):=atan(d/dx Path(x)) as you use slp as the angle in your calculations.

BTW, the velocity diagram doesn't look that realistic to me. Aren't we supposed to see some small up and downs?

[ptc-2126605]

Hi Fred,

I had to use the MCD converter for PTC Mathcad Prime 3.0. I don't think it converted it clearly. Can you send a PDF version over?

Thanks,

Ron

[Fred_Kohlhepp]

This was done in a hurry without a lot of thought. Errors have already been noted.

Use with caution!!

[AlanStevens]

Here's my first attempt using a sungle point model (which is not really good enough for an extended flexible vehicle, but is a starting step).

The profile I get before the vehicle comes to a halt (actually, starts sliding backwards) is as follows:

I've yet to look at Fred's solution, which I'll do now.

Alan

[ptc-2126605]

Hi Alan,

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

Thanks,

Ron