I am in the process of building an antenna mast that can tilt from horizontal (down) to vertical (up). The mast (arm) is 360" and weighs a total of 105 lbs. I need to calculate the amount of force placed on a winch in order to lift the mast (arm) from the down to up position. All the formulas I am finding are for calculating the force required to lift a weight at the end of a leaver. It seems to me that this will not work in my case since the weight is distributed evenly over the entire length of the arm.

I have two options (plans) on how to place my winch. I need to determine which option will require the least effort but also the most stable.

Can anyone shed some light on this? I have attached a diagram.

• You need to calculate the force exerted on the lifting point, then calculate the torque required to rotate the mast. Since this is a kinetic problem, you have to use the energy method to solve the power required to lift the mast 90 degrees.
– r13
Apr 12 '21 at 4:16
• Do you have the option of increasing the length of the support, in either the first or the second scenario? Apr 12 '21 at 13:08
• the winch doesn't care about distributed loads, it only cares about center of mass. Apr 12 '21 at 13:31
• @tigerguy Although in most cases you are right, depending on the speed you are raising the arm, you could run into some discrepancies due to the second moment of area. Had the cable been closer to the center of mass, I'd feel a bit safer that only the center of mass was important (or even futher away to the center of percussion). If the arm is slender enough, you could have significant vibrations while you are raising this. Apr 12 '21 at 15:07
• If you extended the antenna to the left of the fulcrum and added a count gater weight it would make lifting the antenna easier - less force would be required. An analogy of this are boom gates with counter weights.
– Fred
Apr 13 '21 at 9:24

The amount of force, F is the tension in the rope which will indicate the torque in the winch.

In the top case, it is the lever advantage of the ratio of [CG * mass ] of the antenna to the vertical component of F *the connection of the rope distance multiplied by $$\sqrt{84^2+72^2}*(225/72)$$

$$(360"/2)*84"= 2.1428$$

$$2.1428*105lbs= 225lbs.\text{tension of the rope vertical component}$$

temsion of the rope, F, is then:

$$F_{rope}= (225/72)\sqrt{84^2+72^2}=3.125\sqrt{84^2+72^2}=3.125*110.634=345.73lbs$$

.

However

In the lower case, you need to define the distance between the winch and the fulcrum.

If we assume by scaling your sketch it is 60" this case will require higher tension in the rope even if we consider the mass of the antenna to the left of the fulcrum canceling a fraction of the mass to the right.

However, if you could move the pulley to the end of the 72" lever and extend the antenna 84" to the left of the fulcrum then the lower case would be more advantageous.

For both methods, you shall first find the tension, T, by taking moments about the reference joint "A" and set sum M = 0. Then you shall find the reactions, V & H, and power demand of the winch. After that, you can determine which method is more desirable, and the reasons.

If you are looking for just which option would require the least effort then the answer is the second case (PLAN 2).

The help you to understand why is that, do the following mental experiment. Imagine that the support is so high that the fulcrum coincides with the center of the arm. For plan 2 in this scenario, the winch effort to rotate the arm would be almost zero.

(This can be easily proven mathematically, but there is no point because of issues that need to be addressed and are presented on the following section).

## Issues that need to be addressed

Having said the above, there are a lot of issues that you need to consider, before attempting this in your current configuration:

• the vibrational effects
• the strength of the arm

To make an estimate you need to provide:

• the moment of area of the arm (affects strength and vibrational behaviour)
• cross-sectional area of the arm (affects strength and vibrational behaviour)
• rate at which you intend to raise the arm (this will have an effect on the forces)