B Finding the spring constant of a rope

[erobz]

From the cited PDF
View attachment 322755

View attachment 322756

I read that as shock loads, aka, high speed loads from a vehicle going 15 MPH yanking on a vehicle in mud is more elastic with better recovery than slow speed loads (aka, my testing approach with a winch). Am I reading that right?

I think it’s says high strain rates are more Hookean in behavior. You should also notice that the forces developed are higher per unit deflection under higher strain rate. What is the initial strain rate for a 30 ft rope at 5 mph, vs 15 mph. How much do the curves change for your rope?

Also, the higher strain rate curves end more abruptly without plastic deformation. So you can get higher loads, but if they snap they are releasing that energy abruptly too. The higher the load the more likely something on the vehicle could fail possibly sending something through a vehicle of the unsuspecting parties involved like in that tragic story you shared.

The question I have is how are you planning to use this info? Ideally you would use it as a type of safety factor, but when that truck doesn’t come out of the mud it could ( not saying you would) be used as a “push the limits factor” instead; which is less desirable for concerns of safety...IMO.

 

[jrmichler]

I read that as shock loads, aka, high speed loads from a vehicle going 15 MPH yanking on a vehicle in mud is more elastic with better recovery than slow speed loads (aka, my testing approach with a winch). Am I reading that right?

The rope at higher test speeds broke at higher load and less stretch, but there was a large difference in speeds in those tests. Figure 2-6 from that PDF shows the results of strain rates with a range of almost six orders of magnitude. So, let's look at the strain rates of yanking at 15 MPH vs a winch. In order to do that, I make some assumptions. If you have better numbers, then substitute as appropriate.

Assume:
Rope is 30 feet long.
It stretches 15%, or 4.5 feet.
Fast load starts at 15 MPH, or 22 ft/sec.
Slow load (winch) is 1 ft/sec.

Then the strain rates, using the units from Fig 2-6 (percent of sample length per second) are:
Fast: 22/30*100 = 73%/second at the start of pull
Slow: 1/30*100 = 3%/second through the entire pull

Looking at Fig 2-6 with these numbers, there is not much difference between a 15 MPH pull and a winch pull. Note that the pulling vehicle is slowing down while the pulled vehicle is speeding up during the pull, so the rate of stretch decreases during the pull. Does the pulling vehicle ever actually reach that speed by the time the rope gets tight?

Safety question: When a safety blanket is placed on a rope that breaks, how well does it confine the rope/prevent damage?

 

[erobz]

Note that the pulling vehicle is slowing down while the pulled vehicle is speeding up during the pull, so the rate of stretch decreases during the pull. Does the pulling vehicle ever actually reach that speed by the time the rope gets tight?

I think we want to assume worst case here that the stuck vehicle does not move.

 

[erobz]

Assume:
Rope is 30 feet long.
It stretches 15%, or 4.5 feet.
Fast load starts at 15 MPH, or 22 ft/sec.
Slow load (winch) is 1 ft/sec.

Then the strain rates, using the units from Fig 2-6 (percent of sample length per second) are:
Fast: 22/30*100 = 73%/second at the start of pull
Slow: 1/30*100 = 3%/second through the entire pull

Looking at Fig 2-6 with these numbers, there is not much difference between a 15 MPH pull and a winch pull. Note that the pulling vehicle is slowing down while the pulled vehicle is speeding up during the pull, so the rate of stretch decreases during the pull. Does the pulling vehicle ever actually reach that speed by the time the rope gets tight?

Yeah, they don't really start to diverge in that range until the region surrounding the onset of plastic deformation it seems. I suppose that is good news, since the goal is to avoid plastic deformation in the first place. Testing for one speed, but having the other in application doesn't appear like it should have dramatic effect.

 

[B0B]

The rope at higher test speeds broke at higher load and less stretch, but there was a large difference in speeds in those tests. Figure 2-6 from that PDF shows the results of strain rates with a range of almost six orders of magnitude. So, let's look at the strain rates of yanking at 15 MPH vs a winch. In order to do that, I make some assumptions. If you have better numbers, then substitute as appropriate.

Assume:
Rope is 30 feet long.
It stretches 15%, or 4.5 feet.
Fast load starts at 15 MPH, or 22 ft/sec.
Slow load (winch) is 1 ft/sec.

Then the strain rates, using the units from Fig 2-6 (percent of sample length per second) are:
Fast: 22/30*100 = 73%/second at the start of pull
Slow: 1/30*100 = 3%/second through the entire pull

Looking at Fig 2-6 with these numbers, there is not much difference between a 15 MPH pull and a winch pull. Note that the pulling vehicle is slowing down while the pulled vehicle is speeding up during the pull, so the rate of stretch decreases during the pull. Does the pulling vehicle ever actually reach that speed by the time the rope gets tight?

Safety question: When a safety blanket is placed on a rope that breaks, how well does it confine the rope/prevent damage?

Great info.

Does the pulling vehicle ever actually reach that speed by the time the rope gets tight?

Safety question: When a safety blanket is placed on a rope that breaks, how well does it confine the rope/prevent damage?

The pulling vehicle typically slows down very quickly.

I have two safety blankets and I fill the storage pockets with sand, dirt, or water bottles to add more mass. It's a pure momentum play. In most cases the mass of the rope is not that great and the blanket can prevent damage. Worst case is the metal D ring or other heavy metal object breaks off from one of the rigs.

So @jrmichler are you saying I can measure the spring constant of the rope and come up with some numbers that are more meaningful than the WLL and MBS guidelines? Or is another calculation needed? If so, how can I estimate max momentum value?

I think we want to assume worst case here that the stuck vehicle does not move.

Yes, for sure, as that's often the case.

 

[jrmichler]

So @jrmichler are you saying I can measure the spring constant of the rope and come up with some numbers that are more meaningful than the WLL and MBS guidelines?

Yes.

how can I estimate max momentum value?

Get the force vs stretch first. Plot the results. That will tell you if a linear approximation is good enough, or if you need to numerically integrate the measured results. This approach saves a lot of time discussing the various possibilities.

And besides that, I'm curious to see what the actual measured load vs stretch curve for nylon rope looks like.

 

[B0B]

Yes.

Get the force vs stretch first. Plot the results. That will tell you if a linear approximation is good enough, or if you need to numerically integrate the measured results. This approach saves a lot of time discussing the various possibilities.

And besides that, I'm curious to see what the actual measured load vs stretch curve for nylon rope looks like.

Using an amp meter to measure current proved impractical. Using a load cell provide a direct and hopefully better measurement. I'm going to get a 20K lbs load cell. Using a snatch ring and my 12K winch, I should be able to put 20K pounds tension on a rope. The ropes tested all have a MBS of ≈ 30K lbs and a working load (WLL) of only 7K lbs.

I used the data from this youtube video:

None of the ropes are linear so I can't take a couple measurements to get the spring constant. The Smitty and Yankum (far left) are nearly linear. Numerical integration is the only way to measure how much energy they can store.

Using
$W = \Delta KE$
Where W is the work stretching the rope as determined by the trapezoidal/numerical integration.

$KE = \frac{1}{2} m \cdot V^2$

$V = \sqrt{\frac{2W}{m}}$

$V_{\text{mph}} = V_{\text{ft/s}} \times 0.681818$

So using the data for the most expensive rope (and probably the most popular) the Yankum and 4,500 recovery vehicle, it comes out the max safe velocity for a kinetic pull is 1.475 MPH.

The Yankum (10535.5 ft-lbs) has the lowest energy capacity of the ropes above (actually tied for lowest) while the Bubba has the highest at 14572.5 ft-lbs, nearly 50% higher.

But even the Bubba has a Max safe velocity of 1.73 MPH.

These calculations assume a shock load is the same as slow constant load.

There are thousands of youtube videos using vehicles of similar or higher mass, all going over 10 MPH.

The kinetic rope market is a multi million dollar market. Matt's Off Road Recovery makes over a million/year on each of FB and youtube doing dramatic kinetic pulls. I'd like to figure out how I can take measurements for the vendors so they can publish safe data rather than the nonsense they now publish (MBS). But providing such data probably opens me up to liability.

 

[jrmichler]

Your simple calculation has some assumptions:
1) Pulling against a rigid, immovable object.
2) The pulling vehicle is moving at a velocity.
3) The pulling vehicle has neither an engine pulling ahead nor friction slowing it down.

The actual situation is:
1) Pulling an object with mass, friction, and possibly suction.
2) The pulling vehicle has a velocity at the point where the rope gets tight.
3) The pulling vehicle has the engine developing power.

The result is that your simplified calculation is too simple for the real world. But, it does give you a starting point and helps to define the problem solution. This problem needs a numerical solution. The differential equation to be solved is as follows:
1) Two masses - puller and pullee.
2) Either or both masses may be on a slope.
3) The masses are connected by a nonlinear spring - the spring force is a function of the length, and zero when the length is less than the length of the rope.
4) The puller mass has a forward force from the engine.
5) The pullee mass has a friction force that acts against the velocity, and is zero when the velocity is zero.
6) If there is suction, then the pullee mass has a force that is a function of the velocity (or possibly velocity squared).

When solving this type of problem, it is advised to start with the simplest case - no slope, no engine, no friction, no suction. Then add one variable at a time, and make sure the calculation is giving good results at each step.