# Calculation of upward force

Hi,

I just joined this forum and was wondering if anybody can answer my question.
According to the template,

1)Looking at the diagram, when the orni side goes upwards, the lead weight side will go downwards and the angle indicator will move. I was wondering how can I calculate how much force was required to move the orni up if the swinging arm is balanced in the first place? Is there a equation that will allow me to use the angles or distances to the lead weight/orni to measure how much upward force was created?

2) I do not have any equations that I know of.

3)I was thinking of using the angle to calculate the downwards distance moved by the lead weight. Then multiplying the weight of the lead weight by the distance and get the force. Am I going in the right correction?

Regards,
Clifford

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Filip Larsen
Gold Member
I'm not sure I understand your diagram, but yes, torques (force times distance, when those two are orthogonal to each other) do seem the way forward. However, once those two are not orthogonal (like when gravity act on an arm not horizontal) you must also adjust for the angle which requires a bit of trigonometry. See for instance http://en.wikipedia.org/wiki/Torque. To find balance conditions you would set the sum of all torques (the total torque) equal to zero and solve for the forces you need to know about.

If you also want to calculate how much your construction rotates around a fixed axis when various forces are applied, you further need to use Newtons law for rotation, ie. total torque equals total rotational inertia (called moment of inertia) times angular acceleration, which gives a differential equation that can be integrated up to give angular speed and position as a function of time. This requires some amount of calculus to perform.

I'm not sure I understand your diagram, but yes, torques (force times distance, when those two are orthogonal to each other) do seem the way forward. However, once those two are not orthogonal (like when gravity act on an arm not horizontal) you must also adjust for the angle which requires a bit of trigonometry. See for instance http://en.wikipedia.org/wiki/Torque. To find balance conditions you would set the sum of all torques (the total torque) equal to zero and solve for the forces you need to know about.

If you also want to calculate how much your construction rotates around a fixed axis when various forces are applied, you further need to use Newtons law for rotation, ie. total torque equals total rotational inertia (called moment of inertia) times angular acceleration, which gives a differential equation that can be integrated up to give angular speed and position as a function of time. This requires some amount of calculus to perform.

Hi,

Thanks for your reply. It seems that the force you are talking about is not the same one I'm asking. Torque is for rotational around the horizontal axis am I right?
What I am actually asking is regarding the vertical axis. Like for example, my ornithopter side, flaps its wings and produces an upward force and pushes the arm upwards, that would mean that the arm on the lead weight side goes downwards.
So I have an angle indicator at the pivot which will tell me the angle that the arm have moved by in either an up or down direction. I have attached another diagram to show the angle indicator. So when the weight side goes downwards, I will be able to know how much of an angle it moves by.
After I know this angle, if I want to know how much force was applied by the ornithopter side when it flaps and moves upwards, Is it right if I use the weight of the lead weight and the distance it has moved downwards to calculate the force produced by the ornithopter side?

Hope this is explained more clearly.

Regards,
Clifford

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Filip Larsen
Gold Member
I think I understand your construction - now its just the questions I'm not sure about :)

You will not be able to calculate the force from the angle alone. If it really is force you want to find, you must know how fast it rotates. If the masses stay at fixed distance from the pivot point the force will be maximum when the angular speed is maximum. If you are only interested in the average force you only need the time it take for the wing to move from up to down or reverse and not necessarily the angular speed itself.

Perhaps you could explain what it is you are trying to figure out? I mean, why is that you need to calculate this force? Maximum forces and torques are often needed for proper dimensioning of a construction, whereas for performance you would more look at power and work (energy).

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What I am actually trying to figure out if how much lift the ornithopter is providing. As I'm doing a project on ornithopters, I would like to find out whether the flapping wings are providing the sufficient lift to fly the bird, hence the device.

I thought that I might be able to just use normal forces and calculate the lift that the ornithopter is providing by the distance and angle that the swinging arm has moved either upwards or downwards. From your reply, it seems that I might not be able to do that. Can you advise me on how I can go about measuring the lift using the device?

Filip Larsen
Gold Member
I must admit that I have never analysed an ornithopter before, so take the following with a grain of salt. I assume the construction is able to fly (i.e. generating lift) with wings in a fixed position much like a glider plane which continuously descent in order to maintain speed, that is, it uses gravitational potential energy to balance work done by drag in order to keep its kinetic energy constant. With the ornichopter we would now like the full up-down cycle movement of the wing relative to the center of mass to give a net upward force, since we are not able to counter drag like fixed wing planes do by having the engine producing thrust to more or less directly oppose the drag. This means, that over a full up-down cycle of the wing, the work done by the construction on the airmass must be positive.

Looking at the power need, you can overall conclude, that the motor(s) driving the counter weights must be able to deliver at least as much power as the drag power (which is drag-force of the ornichopter in flight times airspeed) plus a bit to cover friction power moving the wing and counter weights if you want it to fly with constant speed without loosing altitude. This is a necessary but of course not sufficient requirement.

Without having done any detailed modelling, but assuming the motor slides the counter weights side to side on its arm using something like a crank-slide coupling, it seems that the cycle speed (e.g. cycles per minute) of the slide must somehow match the amplitude of the slide, e.g. the faster the motor slides the weights from side to side the farther it has to slide them in order for the torque induced by gravity being able move the wing completely up or down at the same frequency as the engine. Of course, having fixed amplitude on the side-to-side movement of the counter weight and then just control motor rotation speed seems like a much simpler mechanical solution, so I'll assume that it is like that, which then means that it is the weight of the counter weights that should be "adjusted" such that natural cycle time of the wings corresponds to a load and rotation speed of the engine where it delivers maximum power.

To get anywhere near actual performance numbers along this route, one would need a more detailed model describing the precise speed/torque characteristic of the motor and the mass of the various moving parts plus their geometric relationship. With the right data it should be a fairly simple matter to calculate power performance (assuming all the model simplifications hold in real life, of course :)

It may also be that there is some simple measurements that you can perform on (parts of) your construction that will tell you a bit more about how it will perform, but I am not able to think of any right at this moment. Perhaps others here can help?

Many thanks filiplarsen.

How about if I draw the diagram in this way. How would you calculate the work done by the WEIGHT in moving from the original position to the next position given the parameters like angle moved or distance moved?

I think I will assume that the work done by the WEIGHT in moving downwards is caused by the work done by the orni in moving upwards. So they should be the same.

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Filip Larsen
Gold Member
The problem is, that while you can calculate the work done by gravity on the weight moving down (that will be height * mass * g) you need to know the angular speed in order to know how much of this work is going into the rotating masses and how much is going into drag forces (from air) from moving the wing at a speed. Look at it this way, at the bottom or top of the each stroke, the wing will (for a fixed position of the weight) be stopped at some maximum angle by the construction and all (or most) the rotational energy of the weight and wing will then be transferred back to the construction structure (most like mechanical "shock" that will be dissipated as heat). One way to avoid loosing energy to the structure at the stop is by moving the weight near the end of each stroke in such a way that gravity will stop the rotation before the stop is reached. And this means you have to analyse the work put into moving the weight up against gravity. Alternatively your wing arm could be constructed with a rotational spring or other flexible structures to allow the wing to recover some of its rotational energy near the end of the up-stroke when it begins its down-stroke, or visa versa. But then you would have to include the springs into your analysis if you want to know the net work.

I have a hard time seeing that you should be able to derive the performance of the bird simply by measuring the angle of that up-stroke you mention. To me it still seems that you would need a fairly complete model of the (electro-) mechanics required to make the full cycle of the wings (i.e. an up-stroke followed by a down-stroke back to same initial condition) and possibly also a model of the aerodynamics of the wing in order to figure out the net work for each cycle. This is very similar to analysing any cycled engine where you need to include all cycles to calculate total work.

But don't let this "lack of theoretical support" stop you. You can get far by practical experimentation and I'm sure there must by plenty others that have practical experience with ornichopters (like in RC clubs or similar) that you may be able to contact.