Help with lever formulas.
April 18, 2010 6:41 PM   Subscribe

Mefi engineers please help me. So my theatre company might be doing a show that requires a set to tilt back and forth. I need help figuring out the math for fulcrums and lever distances.

So one idea we were talking about is basically a teeter-totter with one extra long arm so it can be tilted from off stage. If for example the set is 20 feet wide and weights 1500 pounds with 800 of it to the right of the fulcrum and 700 to the left along with the lever handle how long does the handle need to be for 80 lbs of force to be able to push down on the lever and tilt the set? What if the weight is even across the fulcrum? Obviously this is purely in the theoretical and profesionals will be consulted if and when we build this but I need to figure out some base ideas. Thanks
posted by Uncle to Science & Nature (18 answers total) 1 user marked this as a favorite
What on earth are you putting on a teeter-totter that weighs 1500 pounds?

There's got to be a better way to achieve the effect that you're looking for without constructing such a large and dangerous contraption.
posted by schmod at 7:00 PM on April 18, 2010

Will the weights be fixed securely or are actors going to be standing on this?
posted by bonobothegreat at 7:07 PM on April 18, 2010

There are a huge number of engineering concerns you are omitting in your description. I think you're going to need an in-person consult even to get a handle on the problems you need to take into account, forget about the solutions. For example...

  • You're going to be be putting structural members that are, in usual circumstances, either lghtly loaded or completely in compression under unusual loading -- tension, torsion, etc. Nails work great to tack things down that will be compressed together anyway, are kind of crummy in shear, and usually totally crap in tension.
  • You almost certainly need to add damping (eg, shocks) to prevent this thing slamming down on one side or the other. Having it balanced enough so that a stagehand can operate it will probably mean that the weight of an actor moving from one part to another will significantly change the balance.
  • How are you going to keep the stage from twisting, even a degree to two, from side to side? Even a little off-axis motion, with that loading, will likely shear your fulcrum right off the stage.

  • posted by range at 7:10 PM on April 18, 2010

    This depends on where the weights are with respect to the fulcrum. It also depends on the weights being in fixed positions.

    If you have a fulcrum, and the weight wR to the right at distance R, and the weight wL at distance L1, and a lever of distance L2 to the left, with a force of 80 lbs, then ...

    wR * R = wL * L1 + 80 lbs * L2

    I think, it's been a long time since mechanical engineering, and that plus the possibility of HTML errors means you should check with a pro before assuming my math is correct.
    posted by zippy at 7:10 PM on April 18, 2010

    I should probably have phrased things a little differently. The bigger point is that the purely theoretical answer to your stated question is, sure, it will work. But there are many, many questions buried within your question (eg, can you support your entire set on a point instead of a flat plane; can it withstand tension and torsion; can you properly constrain its rotation to a plane; etc.) that have answers that are not nearly as trivial.
    posted by range at 7:15 PM on April 18, 2010

    What show is this?

    if it were up to me (having never engineered such a set, but having helped construct a two-story revolving set that pivoted around an anchored pole for Noises Off!), I wouldn't look at a teeter-totter so much as a set that can be lifted up from either side to create a ramp. Or one side only, if you only need one side of tilt.
    posted by Madamina at 7:53 PM on April 18, 2010

    Another question is how many times does this happen. Once a performance for 2 techs 2 dresses and four performances or ten times a night for a five week run (it makes a big difference.)
    posted by leafwoman at 7:54 PM on April 18, 2010

    ... also does the floor tilt, do the walls tilt, the floor and wallls tilt, does it have working doors on it, is the tilt .5 degrees, 10 degrees, does it tilt in the midst of scenes and if so how fast or does it only tilt during scene changes, does it have a dynamic load on it (dancers, multiple actors crossing back and forth) or is it a single actor sitting center stage. There are more questions as well.
    posted by leafwoman at 7:59 PM on April 18, 2010

    Obviously this is purely in the theoretical and profesionals will be consulted if and when we build this but I need to figure out some base ideas.

    OK. For a start, what needs to be tilted - a backdrop, or the platform the actors will be working on?
    posted by flabdablet at 8:05 PM on April 18, 2010

    What if the weight is even across the fulcrum?

    If the weight is evenly distributed then the force required to move the fulcrum depends on the friction of the bearing and the inertia of the load. The friction depends on the design of the bearing (surface area), the condition it's in (e.g. recently greased), and how much weight it's supporting. Inertia depends on the rate of acceleration and amount and distribution of mass. Since the fulcrum is not at the center of mass the inertia will have a rectilinear component as well as a rotational component, but for small enough angular displacements you can probably approximate it as purely linear. And if the rate of acceleration is slow enough then you can ignore the dynamic loads and let friction dominate, where "slow enough" greatly depends on the amount of mass.
    posted by Rhomboid at 9:08 PM on April 18, 2010

    I was just guessing on the 1500 lbs but idealy the platform of the set with actors and the backdrop needs to tilt back and forth maybe a degree or degree and a half about 10 times during the show which is going to run for 5 weeks. I'm guessing that a people think a teeter-totter is a terible idea.
    posted by Uncle at 9:24 PM on April 18, 2010

    It also needs to be quick tilts back and forth. The script calls for the world to tilt and for two of the actors to be thrown of stage while two others hold on and stay on stage.

    Thanks for everyones help so far.
    posted by Uncle at 9:29 PM on April 18, 2010

    Depending on your budget, carpenters, shop resources, and the like, it's sounding like the giant teeter-totter is a bit impractical. Perhaps a couple of lights with gobo rotators and/or rotating prisms along with a sound effect could produce the desired result. Alternately, perhaps the set has one or more digital projections involved which tilt?

    Another scenic option might be a turntable which rocks back and forth, though a large turntable is a royal pain to build too.

    I don't know if your theater has a fly system, but if so, perhaps you could fly in a beam of some kind for the actors to stand on. Fly out one side a foot or two, and let two of the actors tumble into the wings while two hang on or jump on to the deck.
    posted by zachlipton at 10:03 PM on April 18, 2010

    For one and half degrees of tilt, you could easily set the whole thing on a single knife edge bearing (or fulcrum and receiver), made of an appropriate chunk of equal leg angle iron as the "knife edge" pointing up from the stage floor, and various bearing points made of flat steel with a grove milled in, to rest on the "knife edge". This is a very cheap, very low friction bearing design, with high load capacity, which works for you because of the low angle of motion needed.

    The lever arm length needed to keep the rocking force below 80 pounds will depend on the distance from the fulcrum point that weight is effectively applied, and how much weight is there. If you have several points of application of weight, at various distances from the fulcrum point, you sum torques to arrive at the net force you have to counter, and then create a length of lever arm sufficient to apply that amount of counter-torque, while keeping the applied force to under 80 pounds.

    But frankly, for the simplest mechanism, I'd just get a couple of automotive floor jacks (2 ton capacity jacks cost about $25 each at Walmart), one for each side of the set, and do some dry runs to establish the maximum needed lift distance on each side. Then weld some sturdy limit stop straps for the jack arms from angle iron (so that no stage hand gets over enthusiastic and lifts the whole set off the knife bearing!), and then have 2 cooperating stage hands rock the set back and forth, in opposite actions of pumping lift and valve release lowering, with the valves and jack handles providing a lot more force multiplication than you'd ever need; that way, if an actor is in the wrong position one night, or you have a stand-in that weighs a lot more than the regular actor, you don't have to worry - the hydraulics in the jacks take care of it, pretty painlessly, from the stage crew's point of view. You should be able to easily and safely rock the set in under 1 second, each direction, all night long, if you liked...
    posted by paulsc at 11:42 PM on April 18, 2010

    I would look for a flatbed trailer of some sort, or maybe a boat trailer, and modify that. It should be able to support a ton or two, while being moved, without a problem. If you don't modify it too much you can resell it when you're done. Try junkyards, or maybe you know an old hillbilly.
    posted by alexei at 12:01 AM on April 19, 2010

    Been involved in tilting a whole house 15 degrees. An 18'' diameter metal pipe, about a 1/2 or more thickness. is under the floor of the whole set. It has welded braces that are like flanges along the top that allow joists to be run bolted to these plates, securing a base platform on top of the pipe assmbly. The joists and the whole floor assembly rest on and are bolted to this central pipe. Very large pieces of lumber are laid out on the floor below, and braced together. there is a round notch cut in the these, that fits the shape of the bottom of the round pipe, which sits in this notch. The notch is well greased. The solid-based platform/floor allows for a slab-on-grade style house to be built on top of it, but as pointed out above, its one thing to rock the ground the house sits on, and another thing to expect stairways and arched door frames to hang together when they were never intended to be stable off kilter. All the welded iron braces, kind of like flying buttresses seen from out side the house, were at least as much trouble of the pivoting central pipe
    posted by StickyCarpet at 2:56 AM on April 19, 2010

    If I understand your description correctly, you're interested in building a teeter totter with the fulcrum at center stage, with uniform loading of 800 pounds stage right and 700 pounds stage left. You're interesting in tilting it about 1.5 degrees or so.

    If the loads are uniform, you effectively have 700 / 800 pound point loads 5 feet from the fulcrum. That means to tilt it just by pushing the edge of the stage (10 feet from the fulcrum) you would only apply 50 pounds of force (700*5 - 800*5 +f(edge)*10 = 0 ).

    This, I think, underscores the real problem with the teeter totter approach - even a 100 pound actor standing 5 feet left of center would tilt the stage (or, a 50 pound actor entering from stage left). To succeed with this approach, I think you would need to lock the stage in position when not in motion, and trust your actors to very accurately hit their marks (balancing the stage) before trying to tilt it. Sounds hairy. Also, watch your fingers and toes when the side of the stage slams down ...

    I don't really see a problem with rigidity, if you overbuild the stage enough. A ten foot cantiliver is not a big deal. The iron bar / pipe approach sounds good to me.

    other important data:
    1.5 degrees translates to about +/- 3 inches (google: tan(1.5 degree) * 10 feet in inches), meaning the fully tilted stage left would be 6 inches higher than fully tilted stage right. This would require a 3 inch diameter iron bar (i.e. half of the height at the end).

    good luck!
    posted by aquafiend at 6:53 AM on April 19, 2010

    I think your answer is going to be moving scenery and actors...acting.

    I am a civil engineer, and while this is possible, it's expensive, dangerous and a lot of work.
    posted by electroboy at 7:30 AM on April 19, 2010

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