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*Same force but two moments?*

  1. Dec 13, 2013 #1
    I have been boggled by something for a while now. It pertains to the forces acting on two cranks in an opposing piston engine.

    So let's just assume the pressure remains constant in the cylinder(for simplification). Now half way through the cycle one piston is acting on a 3" moment arm with a sin of 1(90deg), the opposing piston is also acting on the other crank, with a 3" moment arm of sin of 0.5(30deg).

    Let's assume the internal gas pressure is 200psi and the surface area of both the pistons is 5sq.in. So 1000 lbf is acting on each piston. Now this is where I get confused...

    Is the combined torque magnitude(if the cranks are geared together) compounded? Or how is the total torque output calculated?

    So 1000 lbf on a 3" moment arm with a sin of 1 is 250 lb-ft
    1000 lbf on the opposite crank with a sin of 0.5 is 125 lb-ft

    Since they are geared together what is the final torque output value? Is it 750? That seems wrong...It's wrong to me because to me it's like if they compiled the forces, it would not agree with energy conservation laws. That would be like, the same spring pushing on two moments with a sin of 1 would equal 2 sin total...what the heck am I missing here? I understand that if the forces stay the same, then the only difference is the distance traveled by the pistons. So the GASES are doing 2x the work(roughly), so the work would be more, but the torque would be the same with two cranks the same size(if the moments were 90degrees on both)versus a single crank right?

    I don't care about the HP/power/work values. I'm only looking to understand the torque output. Single moments I understand, but double? I can't seem to find any information regarding this process!

    Last edited: Dec 13, 2013
  2. jcsd
  3. Dec 13, 2013 #2

    Simon Bridge

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    Welcome to PF;
    The total torque output is calculated the same way as for any engine.
    Focus on the end result - the mechanism is designed to make sure the wheels (or whatever) turn in the same direction.

    The details will depend on the exact configuration.
    So draw a picture.
  4. Dec 14, 2013 #3
    This is simply from googling. It's simple really, there are many engines like this in use by the navy. What I'm trying to understand, is by adding another crank that is run by the same gas pressure in the same cylinder adding to the total torque? So imagine those two cranks are geared so they connect at a point, just they are rotating in opposite direction. I think what they use is a vertical shaft and pinion gears.

    SO, my understanding is since the total piston travel is now 2x that of an engine of the same size (just with one piston). So the intake stroke sucks in 2x as much air, and assuming the expansion forces are equal throughout the entire stroke as a similar engine with only one piston/crank that has the same moment arm, just 1/2 the stroke/one crank.

    I guess I should clarify my question...Does the force of the gas acting on both piston faces compile to create a SUM final torque on the final drive gear? Does 250 lbf on one crank(moment 1) add to 500lbf(moment 2) on the opposite(directly connected crank) to create a sum total of 750 lbft of torque?

    This can be even more simplified to ask, if it takes 100 lbs to compress a spring, and that spring will (lets assume) push back 100lbs for it's entire expansion(not realistic but for simplification).

    1) If one side of the spring is mounted to a static pivot, and the other end is pushing on a 3" moment at 90deg, then that 100lb force would equal 25 lb-ft Torque

    2) Now that same spring is now acting on another crank instead of being attached to a pivot point, therefore the spring must now travel 2x the distance(2x the work) but is also acting now on two moment arms, both sin 1, both 3". Does the torque stay at 25 lb-ft? Or is the torque combined when those two cranks are essentially driving eachother(so 50 lb-ft)?

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  5. Dec 14, 2013 #4

    Simon Bridge

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    It's not clear what you are comparing with.

    Say you just had two regular cylinders using half the fuel and also half the size ... both driving the same crank as will a straight engine say. What difference does it make?
  6. Dec 14, 2013 #5
    It should be clear to what I'm comparing with as I've explained it above.

    Comparing a dual crank design, to a single crank that has a piston surface of the same diameter, with a moment arm the same length(3"). The only difference(minus added friction/etc) is there are now two pistons acting on the same load. So I'm trying to understand the static friction when one piston is at 90 degrees, and the other one is at 30 degrees.

    So piston one is pushing 250lb-ft of torque, and piston 2 is 125 lb-ft torque. So imagine that there is 2x as much gas, but assume the internal pressures are the same throughout the expansion cycle for both a single cylinder vs a double.

    SO, my question again, does the torque combine to create 375 lb-ft of total static torque? Or is the combined magnitude the same as a single piston design so 250lb-ft of torque? 383 views and no answer? lols.
  7. Dec 14, 2013 #6

    Simon Bridge

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    Surely you want to know if you are better off in some way by sharing a cylinder?
    (Apart from the balancing.)

    The idealized equivalent non-shared approach would involve putting a wall between the two pistons, keeping the rest of the geometry the same. (this will need small variations to the layout.)

    Half the fuel is delivered to each of two cylinders for combustion - delivering the same total power to drive the machine. Now you have an equivalent system for comparison.

    You will always be able to come up with another engine design to do something different.
  8. Dec 14, 2013 #7


    Staff: Mentor

    Yes, torques add. The total torque on an object is the sum of the individual torques.

    Your question is very long and unclear. Shorter questions with attention to clarity tend to get answered faster. However, your thread is not particularly far "off-center" in terms of views and posts.
    Last edited: Dec 14, 2013
  9. Dec 14, 2013 #8
    Ok, I just couldn't imagine how if two torques were at the same magnitude how it would become a SUM on the final drive gearing. I suppose I was confusing MASS with FORCE. Like if you weigh yourself one foot at at time and you were balanced, both scales will only show 1/2 your true weight.

    I confused myself, I guess I could have just reversed the process using fictional numbers to figure out what forces are required to cancel out the force acting on the pistons.
  10. Dec 14, 2013 #9

    Simon Bridge

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    Excuse me - I had to make sure I understood you ... I know you think you are being perfectly clear but you know what you mean to say before you write it while I need to be sure I have it right the long way round.

    A torque is just a turning force - a twisting.
    Imagine one of those bulkhead doors in old submarine movies - the kind with the bog wheel in the middle.
    One person may have trouble turning it but two people find it easier - the two torques add together.

    If the second person tries turning the wheel the opposite way, however, the torques will subtract.

    If those two torques are in the same direction, about the same axis, then the net torque will be 400lb-ft.

    I don't know for sure what you mean by "sine of 1" and "sine of 0.5" though so I cannot be sure that I have answered the question you mean to ask.
    the sine of 1 is 0.84147 if that is 1 radian, 0.17452 if it's 1 degree, but it could mean that the sine of some angle is 1 ... so that angle would be 90deg or pi/2 radians. But if that's what you meant, why not say so? Of course you still have to say what the angle is in relation to.

    "moment" is not normally measured in units of length.
    It is usually a synonym for torque.
    Do you mean a 3" moment-arm?
    At 90deg to what?
    Should we guess?

    And it is not clear what the springs have to do with the system under investigation.
    So, you see, this is hardly a simplification.

    It sounded to me like you wanted to see if there was some mechanical advantage to this configuration of two pistons ... but it seems you just wanted to know if the pistons add. They do:

    If you set two engines to drive the same shaft, you get twice the torque as from one engine alone.
  11. Dec 15, 2013 #10


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    Forces and torques just add vectorially (i.e. the directions count). If they are applied in 'step' you will get a pro rata increase in power too.
    BTW, (re: first post) Principles of "Energy Conservation" do not apply here. You can get more or less efficiency but that's another matter. The only conservation law that can be applied in cases like this is Conservation of Momentum.
  12. Dec 16, 2013 #11

    Yes sorry sine of 1 as in the conrod angle of 90 degrees(not radians) to the axis of rotation. The length of the lever arm being 3" from the point of axis, to the point of force. Altogether, the "moment arm". So at 30 degrees(Sine of 0.5) the moment arm acts as a 1.5" lever arm. It's easier for me to imagine the angle of a force perpendicular to an axis, using sine to reduce the size of the "radius" to calculate the magnitude of force, thus the torque in lb-ft.

    I understand how having two separate pistons (say a 2 cylinder vs 1, same piston area, same stroke) would equal 2x the torque(static torque, not calculating inertia or rotational mass)if both pistons were acting at the same angle on the crank at the same time(Not considering gas expansion rates/etc).

    Anyways, I couldn't understand it because the dual crank design was pumping out the same numbers as a single crank design where the radius (lever arm) was twice the length. So trying to understand how the same force just acting on two lever arms instead of 1 was somehow magically doubling the mechanical advantage. So I assumed it would half the force magnitude. But now I see that the distance traveled is 2x, and when calculating as POWER not torque, the equation does require twice the torque to have a balanced equation.

    By the way the compressed spring explanation does make sense, because like using fictitional numbers(like static pressure in the cylinder throughout the cycle) is comparable to a compressed spring where it's outward force is static through it's entire expansion length.

    So a spring acting on one crank(one side pushing against a solid object/wall/pivot) and the other side acting on the lever arm, the spring will expand (from TDC, to Full expansion) exactly 2x the radius. Whereas that same spring if instead of pushing on a wall, is now pushing on another lever arm exactly the same as the first one(just reversed), the spring will now move twice the length, or 4x the radius of 1 crank.

    So anyways, I was confusing myself, thinking that if these two cranks were geared together, that the final torque would only be as high as the max torque that has been applied(the same as having one crank). But now I realize I should have just done the math properly using power, as torque and thus force can be calculated by doing the equation backwards.

    So to sum this up, in simplified terms. A dual crank design, when lever arms are equal, will act like a single lever arm that is twice the length. The pistons move twice the distance, just like how a lever twice the distance from the falcrum point, will require the half force but travel twice the distance perpendicular to the falcrum/axis of rotation. Therefore allowing the weight on the opposite side of the lever, to also be twice the distance from the fulcrum if the force on the end remained the same. Therefore twice the torque. So by using 2 cranks, you can have a 2:1 gear ratio where 1 revolution of this design, will be the same as 2 revolutions in a single crank design. So the same effect as having a single crank design with a crank that is twice the radius.

    So does anyone agree then that this opposing piston design allows for much more compact engine design? Not only is there less thermal loss(there is no head), the stroke size can be smaller as well as piston diameter. Only problem is the height of the engine(or width), and added friction on main bearings and subsequent gearing.

    I still prefer the boxer engine designs because the design allowing them to be balanced(less vibrations/less bearing stresses), but these opposed engines seem like they may be more efficient, and therefor may play a big role in future engine design.
    Last edited: Dec 16, 2013
  13. Dec 16, 2013 #12


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    Torque is not power. Engine design is based on much more than just one detail. Multiple cylinders are not chosen just to get a different torque. It's done for balance, smoothness and a host of other reasons.

    The Maths associated with Moments was sussed out long ago and speaks for itself. It doesn't benefit too much from a chatty approach.
  14. Dec 16, 2013 #13
    Care to clarify?

    IS not HP = Torque x 2∏r x RPM/33000

    OR HP= T x RPM/5252

    So HP is useless really. That is why I didn't really want to use a power equation because it is simply a factor of Torque anyways. Without having torque you can't have HP numbers. IT's just a fictitional way to explain Work in time. So anyways guys/gals/whoever I came here just to clarify from more experienced folk on certain issues I had with my math. If I wasn't looking for clarification I'd be selfish and unable to confirm my numbers.

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    Last edited: Dec 16, 2013
  15. Dec 16, 2013 #14


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    "HP is useless" ????? You quote the formula in the line above that statement. What does that formula mean to you?
    Engines do Work. That's their raison d'etre. The rate they do Work is the Power. Give me any engine and I can give you a gear box that will produce you any Torque you want. The only downside of that is that the rate of doing work will not be more than the engine can produce and the speed at which that torque can be produced will be limited to less and less as the torque is increased. Power is Torque X Revs - as you wrote. Then take some off for efficiency.

    There are more text books on the Basics of Mechanical Engineering than I've had hot dinners. Take your pick; they will all agree where it counts. Much of the maths involved revolves on little more than School Algebra. You don't need to get into Calculus until you get to significant depth.
    I googled "Free engineering ebooks" and got dozens of links.
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