# Force required to accelerate upward against gravity

• Big Tommy C
In summary, @PeroK has found an equation that calculates the force needed to accelerate an object upward against gravity. The equation takes into account mass, acceleration, and gravity, and provides a figure for the required force.
Big Tommy C
So I am working on a project where I am attempting to accelerate an object upward Against Gravity but I am having trouble figuring out the math behind the force needed to do this here is what I have come up with so far,my apologies I am not very good with math

I found this equation
W=m(a+g)y

W=work required
M=mass of object
A=acceleration of the object
G=acceleration due to gravity
Y=displacement of the object

Is this the equation I should be using? I can't really figure out what my acceleration due to gravity would be since I'm going against gravity, but here is my scenario.

The object starts from a stationary position and accelerates upwards with a constant force.

Mass of object 1814kg
Acceleration 9.8m/s2
Displacement 1.291 meters
Time to cover 1.291 meters .5 seconds

Work is force * distance, and force is m(a+g), so yes, that equation works fine.
g is fixed at 9.8 m/sec near sea level, so you're essentially accelerating (an elevator car say) at a proper 2g to 4.9 m/sec in half a second.

Big Tommy C
So my equation should be 1814(9.8+9.8) and then multiply that by 1.291 meters?

Big Tommy C said:
So my equation should be 1814(9.8+9.8) and then multiply that by 1.291 meters?
Why do you want to ascend ##1.291m## in precisely ##0.5s##?

That corresponds to an acceleration of ##10.328 m/s^2##.

Big Tommy C and russ_watters
Big Tommy C said:
So my equation should be 1814(9.8+9.8) and then multiply that by 1.291 meters?
What are you trying to calculate? The force you need to apply? And do you want it to stop at the top, or is carrying on flying upwards acceptable? Note that gravity hinders you starting it moving but helps you to stop it, and how much braking force versus accelerating force you can apply will probably affect your solution.

Note that @PeroK's solution assumes you aren't stopping the mass at the top. The necessary acceleration is going to be higher if you want to stop it again but use the same time. Note also that moving around two metric tons (edit: I meant "aroun" in the sense of "about" two metric tons - on closer inspection, the specified mass turns out to be exactly two short tons) through this kind of distance in this kind of time is a significant engineering challenge.

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Big Tommy C, russ_watters and PeroK
Big Tommy C said:
So I am working on a project where I am attempting to accelerate an object upward Against Gravity but I am having trouble figuring out the math behind the force needed to do this here is what I have come up with so far,my apologies I am not very good with math

I found this equation
W=m(a+g)y
You said you want to calculate the force for a given acceleration, so you should use the equation for force vs acceleration: f=ma. For vertical acceleration, the only thing you need to change is to add gravity to it, which is a constant acceleration of 9.8m/s2: f=m(a+9.8)

Mass of object 1814kg
Acceleration 9.8m/s2
Displacement 1.291 meters
Time to cover 1.291 meters .5 seconds
You can't specify an acceleration, you have to calculated it...which @PeroK did for you. That's using the distance/velocity/acceleration relations. From there, plugging into f=ma yields a force of 36,400 N.

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Big Tommy C
What profile is your acceleration going to follow ? Going to max it out and bang into the stop ? or cut power during travel and let the mass go ballistic and coast to a zero-zero stop.

Ibix
The mass will be driven via a hydraulic cylinder, the hydraulic system will shift into a "neutral and the mass will decelerate, I think I miscalculated the acceleration earlier, but yes gravity will stop it.

Right - so do you need to reach 1.291m height at zero speed? Or do you just need to reach it in half a second and you can let the mass carry on flying upwards?

Big Tommy C said:
The mass will be driven via a hydraulic cylinder, the hydraulic system will shift into a "neutral and the mass will decelerate, I think I miscalculated the acceleration earlier, but yes gravity will stop it.
That sounds like engineering to me! This is 1800kg for real?

Ibix said:
Right - so do you need to reach 1.291m height at zero speed? Or do you just need to reach it in half a second and you can let the mass carry on flying upwards?
So yes upon further consideration I do need it to stop roughly around that height I was planning on leaving a little more height above for decelerating but I hadn't yet taken Into account the deceleration distance

PeroK said:
That sounds like engineering to me! This is 1800kg for real?
Yessir, the force needed to achieve this can be done with hydraulics as long as you take everything into consideration and design the system appropriately, accumulators can be used to generate massive flows at high pressure and so forth

Big Tommy C said:
So yes upon further consideration I do need it to stop roughly around that height I was planning on leaving a little more height above for decelerating but I hadn't yet taken Into account the deceleration distance
It'll come back down again. You better take that into account as well!

Big Tommy C
Big Tommy C said:
The mass will be driven via a hydraulic cylinder, the hydraulic system will shift into a "neutral and the mass will decelerate, I think I miscalculated the acceleration earlier, but yes gravity will stop it.
The mass sounds like a loaded elevator, but 2g is a bit harsh for the public, so maybe something else.

Anyway, is there such a thing as 'neutral' for a hydraulic system? It's not like they can just throw the valves open. The pump still needs to run even when doing no work. What do I know? I'm the wrong kind of engineer.

russ_watters
Your 0.5 second requirement. That is to reach the 1.291 meter height? Or to come to a stop after having reached the 1.291 meter height?

If it has to come to a stop and if you want to use gravity to stop it, you have an impossible problem. Not even an infinite acceleration can get you there and stopped in time. You'd spend a minimum of 0.51 seconds coasting to a stop at the lowest feasible starting velocity. If you need it stopped within the 0.5 seconds, it has to be a powered stop.

russ_watters and Ibix
The force is easy for hydraulics, but the speed may not be. But also since it is hydraulics and I compressible the acceleration and deceleration can be very large as long as the equipment doesn't tear itself apart. But anyway, I'd research high speed hydraulics to see if this is in the range of what is currently done.

Yes to answer everyone's replies, I was in the field today when I posted this and made an error from my original design, the minimum displacement of the weight will be 0.9144 meters, sorry about that, and I think I found the same answer simply by doing my f=ma and then adding the weight of the object being accelerated to that for the final answer of force. Is this a fair way of coming to this answer?

To answer the questions about the hydraulics @Halc, technically no there's no neutral, its an in-compressible fluid for all intents and purposes,if actuators are moving the fluid must go somewhere, actually WILL go somewhere no matter what lol, Basically you use an arrangement called a Regen valve circuit where the fluid from the collapsing end of the cylinder in added to the extending side to increase efficiency, this will only work on the rod end though because the volume of the blind end is more than the rod end, if you reverse you won't have enough volume to fill the blind end from the rod end so a "neutral" circuit must be designed to feed in the missing volume in order to keep a void from forming. As for russ_watters, yes the force is easy under normal circumstances but in the high speed application the system must be designed to handle at or near the desired flow, any excess will snowball the cost of the system, the speed can be achieved via nitrogen charged hydraulic bladder accumulators and fast acting 2 port logic valves, an accumulator can easily supply 250 gallons per minute for a limited time, however the pressure will degrade as it empties out, hence once again everything must be sized correctly.

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This is very doable, but there are a number of factors that need to be considered.

When moving heavy objects at high accelerations, it is usually best to design the motion profile by ignoring gravity. Include gravity later in the design process when sizing actuators. The optimal motion profile for a fast move is usually constant acceleration, also known as triangular velocity. Accelerate half way, then decelerate the other half.

You want to move a mass 36 inches in 0.5 seconds. With a constant acceleration motion profile, that's an acceleration of 576 in/sec^2 (1.5 G). The required force to accelerate up and decelerate down is (576 + 386) X 4000 lbs / 386 = 10,000 lbs. The peak velocity will be 0.25 seconds X 576 in/sec = 144 in/sec. The peak power will be 10,000 lbs X 12 ft/sec = 120,000 ft-lbs/sec = 218 hp = 163 kw.

This move could be made with hydraulics or servomotors. Looking at hydraulics, the peak force is 10,000 lbs. If we design for 2,000 PSI, the hydraulic cylinder needs 5 square inches piston area. While a 2.5 inch bore cylinder has this area, the high force and long stroke require a large enough rod and a cylinder stop to prevent buckling. A larger bore may be required.

Assume a 3 inch bore cylinder. The piston area is 7.07 in^2. The peak velocity of 144 in/sec requires a peak flow rate of 7.07 X 144 = 1000 in^3/sec = 4.4 gallons/sec = 265 GPM.

Because you are following a motion profile, the hydraulic circuit needs servovalves, and a controller with position feedback. Attempting to move a mass this heavy at these accelerations and speeds with ordinary hydraulic components WILL cause problems. I know of a case where the engineers tried to do just that. They were rotating a mass weighing about 2000 lbs through an angle of 180 degrees in less than one second. Because they thought that an internal cylinder cushion could stop the move, and failed to do the calculations, the entire mass broke off and crashed to the floor. In the customer plant.

You need to design for an E-stop (emergency stop). If the E-stop opens the hydraulic valves on the way up at beyond about the 40% up point, it will crash into the upper stop, then fall and crash into the lower stop. Similar on the way down, only it will hit the lower stop at even higher speed. If the E-stop closes the hydraulic valves while it is in motion, the momentum will destroy something. It may destroy the cylinder, or just blow a hydraulic hose. An uncle of mine was standing near a hydraulic hose that sprung a pinhole leak. The jet of hydraulic fluid injected into a finger tip, and went up through his arm past his elbow. The doctors were able to save his hand and arm, but it was permanently partly crippled. A catastrophic leak would be much worse.

You also need to design for a crash. Any motion control system can fail. Failure modes include hitting an end of travel at full speed. In either direction. You need to deal with both the resulting momentum and kinetic energy.

This post is not an engineering analysis, but an outline of some of what needs to be done to make this system work. This job should get a full and complete FMEA before buying any parts.

russ_watters, berkeman and Big Tommy C
jrmichler.

Well said sir, so basically I planned on keep this a constant acceleration via flow control rather than pressure control, the system will run at 3000 psi, and should not need any advanced electronics or servo valves, I already encounter equipment in my field that exceeds these velocities and masses with simple on off spool valves on the pilot end, using logic valves you instead use control orifices to limit the speed in which valves open( mainly to stop destruction of the valve)

In the design the the stroke will be limited mechanically by a cushioned implement on both sides of the stroke and the overall cylinder stroke will exceed these limits to ensure the cylinder is never the stopping implement, additionally the cylinder will be affixed to the mass with a cushioned implement as well to help reduce some shock in the system, but I am planning on timing the valve solenoids in a fixed setting so that they can let the mass coast upward at just the right time and stop with little impact against the physical stop at the top,

as far as the valves and exploding hoses the system will always be connected to a system relief and an anti shock accumulator, and Yeah hydraulic fluid can be some dangerous stuff, if not treated immediately limbs can be lost, I have been a Hydraulics and heavy equipment Technician for about 6 years and have seen some spectacular failures lol.

Honesltly I could talk hydraulics all day, if you have more suggestions or you think I am going down the wrong path lmk

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I don't think, I know, that you are heading for some expensive surprises.

The acceleration due to gravity is 386 in/sec^2. The minimum acceleration to make your move is 576 in/sec^2. That means that it cannot coast to a stop on the upward move. You need a controlled downward force of 2000 lbs to slow it to a stop. Similarly, the first half of the downward move is a downward force of 2000 lbs. You have to push down to get the mass moving fast enough to make the move in your specified time.

The system you describe can control the acceleration to some extent. You are trying to shift a valve spool from closed to open in 0.25 seconds. The goal is to increase the flow rate from zero to the desired value (265 GPM for a 3" cylinder) in 0.25 seconds, and that the flow rate be a linear function of time. You are trying to do this with a valve that does not have a linear flow vs position characteristic, and do it while the hydraulic pressure is decreasing. Any nonlinearity of flow vs time will cause higher peak acceleration. Higher peak acceleration causes increased forces and pressures.

Hydraulic components rated for 3000 PSI will tolerate higher pressures once in a while. If they are regularly subjected to higher pressure, you can expect short lives from cylinder seals, hydraulic hoses, and hydraulic valves.

I have experience with moving a 900 lb mass 36 inches vertically at 500 in/sec^2, for a move time of 540 msec. Since it was done with servomotors, the motion profile was completely specified, and the move was made without shaking, banging, or slamming. Those machines make the up and down move up to 16 times per minute, 24 hours per day, 7 days per week, and run for years with minimal maintenance. I have not seen spectacular failures because we designed these machines such that the components were not overloaded. And when we designed them to run at a speed, they ran at that speed. All day, every day, for years at a time.

If you are able to tune your system to make the move without any shaking or vibrating, you might be able to get the same life. But if your system needs to be worked on every month or more, it's because your peak pressures are higher than you think.

Of course, if the 0.5 second move time is merely an aspirational goal, and the real goal is 1.0 or 1.5 seconds, then the whole project gets much easier.

When moving masses fast, the goal is to make the move smoothly. If you see any sign of vibration, slamming, or banging, you can expect that it will need a lot of maintenance.

russ_watters, Ibix, berkeman and 3 others
Yes the 0.5 seconds is not a absolute number, I was more trying to work through the math,

this machine design will have adjustable heights, this is the maximum displacement and will probably realistically be in the 1 second + range, as for the valve, this is not a spool valve, it will be run by a poppet logic valve. these valve can react much faster than 0.25 second so I wasn't so much concerned about the window between full open and full close as I was the flow rate effected by the pressure drop as the cylinder goes up,

this time in which the valve can be opened can be reduced or increased via control orifices to fit the profile I want, I haven't looked this far ahead yet because I am still kind of at the ground floor working out the forces required, I am assuming that pressure intensification is inevitable to some degree when moving hydraulics this fast and I had alwayes planned on building the system to withstand 6000 psi running pressure and only run it at 3k. ie use ductile iron manifold, high pressure seals, ect to give it more reliability. But ultimately my end goal is to cycle as fast as possible while retaining reliability,

however in my field it is perfectly acceptable to replace actuators every thousand hours i don't wish to do that, I want the mass to coast to a stop upward but downward I will have to add pressure to exceed 1g this will be where the work is done via kinetic energy.

I do appreciate your input you seem like you have some extensive experience with hydraulics design, I am slowly trying to work through everything and take all parameter into consideration this is kind of just a personal project of mine that may become something more, i will be doing all of the machining welding assembly ect to build it once its finished in cad.

[Mentor Note -- Post has been edited to try to add some paragraph structure to the original wall-o-text, but the result is modulo the lack of sentence structure. Poster has been contacted about this posting style]

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## 1. What is the force required to accelerate upward against gravity?

The force required to accelerate upward against gravity is equal to the mass of the object multiplied by the acceleration due to gravity, which is approximately 9.8 meters per second squared on Earth.

## 2. How does the force required to accelerate upward against gravity differ from the force required to accelerate downward?

The force required to accelerate upward against gravity is greater than the force required to accelerate downward because the object is moving against the direction of the gravitational force.

## 3. Does the force required to accelerate upward against gravity change with the mass of the object?

Yes, the force required to accelerate upward against gravity is directly proportional to the mass of the object. This means that the larger the mass, the greater the force required to accelerate it upward against gravity.

## 4. How does air resistance affect the force required to accelerate upward against gravity?

Air resistance can make the force required to accelerate upward against gravity greater because it acts in the opposite direction of the motion, making it more difficult for the object to move upward.

## 5. Can the force required to accelerate upward against gravity be greater than the weight of the object?

Yes, the force required to accelerate upward against gravity can be greater than the weight of the object. This is because the force required to accelerate upward against gravity is a combination of the object's weight and the additional force needed to overcome the gravitational force.

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