Math Question - Too hard for me

[AC Power]

As an electrician, we do learn some harder aspects of math, but this one is not our thing.

I was wondering if there in an engineer (or mathematician) in here who could figure this out?

I have a scissor lift that I need to drive up a 10' custom built steel ramp to the bed of a pick-up truck. The truck's bed is 36" above grade. Any ideas about the angle I would need to prevent high-centering at the reflex angle (in RED in attached drawing)?

See drawing, and Thanks to anyone who has this type of expert knowledge!

 

[Otis]

Hello AC Power. If the ramp were level with the truck bed (i.e., horizontal), then your red angle would be 180º. We'd like to know by how many additional degrees that angle will have increased, after the ramp has been lowered to grade. That extra measure is the same as it is for the angle labeled 'a' below (in my diagram). Angle 'a' appears opposite a 36-inch side of a right triangle having a 120-inch hypotenuse (i.e., longest side).



Determining the measure of angle 'a' is a right-triangle trigonometry question. There is a mathematical function called 'arcsine' that provides us the measure of such an angle, after we provide it the ratio of lengths 'opposite side to hypotenuse'. That ratio may be written as 36/120.

Using a scientific calculator (set to degree mode), we input arcsin(36/120) and it outputs 17.5 (rounded). We add 17.5º to 180º, to get the measure of the red angle in your diagram.

180º + 17.5º = 197.5º

Now, your question is this: Given the known parameters in the attachment, will the undercarriage make contact with the ramp?

I'm curious. Does the lift have shock absorbers? Is the given clearance with respect to the wheel centers guaranteed through all angles, as the lift inclines (while crossing the bottom of the ramp) and declines (while crossing the top)?

?

 

[AC Power]

Thanks So Much Otis! You've been of terrific help.

In answer to your question: Shock Absorbers? No. And no springs neither. The wheel's bearing assemblies are welded directly to the frame. Its NOTHING like a vehicle, where springs provide independent movement of the axle, and the shock absorbers control the action of the spring (dampener).

If you've any question about electrical (anything involving a wire; AC power, DCpower, batteries, LAN/internet, telephone, fibre, etc....) feel free to ask me. I'd be happy to help you as you have myself.

 

[Otis]

Hi AC Power. Please excuse the delay; somehow, I missed your reply.

To be clear, the 197.5º angle is the angle that you provided (i.e., the red angle formed by a 10-foot ramp, raised 3 feet at one end to a level truck bed).

I understand from your explanation that the ground clearance is fixed. I graphed your given scenario, and it's clear that you need a longer ramp.



A 25-foot ramp would reduce the angle to about 187º, and the lift's weight force would likely push the rear end of the truck downwards a bit, further reducing the angle. It's too small to see in the graph below, but there ought to be an almost 1/3-inch gap between the undercarriage and the top of the ramp, in that scenario. (That doesn't give much wiggle room.)



The more the truck bed inclines, the shorter the ramp needed. I didn't check the numbers, but I suspect that parking the truck on a modest incline or jacking up the front end would not reduce the ramp length much.

Alternatively, you could raise the bottom end of your 10-foot ramp 22 inches off the ground, and build a second, custom ramp that would sit on the ground. (24 inches would be better, me thinks.)

?