1. ## General Engineering Formulae

#### Horsepower (HP)

By definition, 1HP is the rate of work required to raise 33,000 pounds one foot, in one minute. In regards to winches, capstans, and carpullers, the equation we are interested in is:
• Line pull is defined as the amount of force, in pounds, the winch can pull continuously.
• Line speed is defined as the rate at which the winch pulls in the line at full load, in feet per minute.

This calculated horsepower is theoretical, assuming 100% gearbox efficiency which is unattainable in the real world. To find the real horsepower required, use the following equation:

#### Torque (ft-lbs)

Torque can be thought of as a rotational force. 1 ft-lb is defined as the rotational force of one pound of force acting on a lever arm one foot radially from the center of rotation. The equation of torque is:

Knowing the input torque of your electric motor, gear reduction ratio of the winch gearbox, and efficiency, you can find the output torque of the winch:

And finally, knowing the output torque of the winch and the diameter of the drum, you can find the line pull:

Drum diameter must be in inches, and then is divided by 12 to convert to feet, and multiplied by 1.1 to account for the wire rope increasing the pitch diameter where the force is occurring.

#### Unit System Conversion

 US to SI Conversion SI to US Conversion When you know: Multiply by: To get: When you know: Multiply by: To get: inches 25.4 millimeters millimeters 0.039 inches feet 0.305 meters meters 3.279 feet yards 0.914 meters meters 1.094 yards miles 1.61 kilometers kilometers 0.621 miles gallons 3.785 liters liters 0.264 gallons ounces 28.35 grams grams 0.035 ounces pounds 0.454 kilograms kilograms 2.203 pounds pounds(force) 4.45 newtons newtons 0.225 pounds(force) horsepower 0.746 kilowatts kilowatts 1.340 horsepower ft-lbs 1.355 N-m N-m 0.738 ft-lbs in-lbs 0.113 N-m N-m 8.850 in-lbs feet per minute 0.305 meters per minute meters per minute 3.279 feet per minute

## Selecting a Capstan

When selecting a capstan you must know at least two of the three variables in determining a Superior Lidgerwood Mundy M-2000 Capstan model: Line speed, line pull, and horsepower. In using the calculations above, you can determine the third variable dependent on your two known values, and easily select a model using our M-2000 Selection Charts.

#### Line Speed:

If you already have a functioning capstan that an SLM model will be replacing and the line speed is unknown, calculating it experimentally is fairly simple. Start by marking a three foot section of rope so you can easily see where the three foot section starts and ends. Start the capstan or winch and spool the rope inwards. Start a stopwatch when the first end of the three foot section hits the drum and stop the time when the end of the section hits the drum. Record this time, and then use the following equations to get line speed in feet per minute: If this is a new capstan, a standard beginning line speed is 20-30 fpm for most applications, adjusting higher or lower to suit your specific tow.

#### Line Pull vs. Starting Pull:

Another area of confusion is the difference between line pull and starting pull in M-2000 capstan selection. Our capstans are designed with electric motors and gearing to achieve an initial starting pull of 200% of the line pull for a limited amount of time to set the load in motion. This allows sizing and selection of a capstan strictly in choosing a line pull to maintain the load in motion, as long as the force required to start the load in motion is less than twice the running pull. The capstans will not sustain the starting pull for an extended period of time without serious damage to the electric motors.

#### Sample Selection Calculations:

For this example we are going to assume company X is replcaing a capstan currently in use on one of their workboats. All they can find on the capstan nameplate is that the motor is 10HP. They then followed the above method of experimentally finding line speed and found that it took the capstan 5.14 seconds to pull in the 3 foot marked off section of rope. Line speed was found as follows: After finding the line speed, we can then use this value in combination with the motor nameplate horsepower to find the line pull required: So, company X requires a capstan with a line pull of 8,863lbs at a speed of 35fpm. From looking at the selection charts, we can see this lines up closest with the SLM M-2000 model E100-12-179 which pulls 9203lbs at 34fpm.

## Variable Frequency Drives (VFD):

Variable Frequency Drives are relatively new to the market in the scope of winch history, and a great option to add to a winch system. A variable frequency drive installed inline between the AC power source and electric motor will control the frequency of oscillation of AC power being supplied to the electric motor, thus being able to infinitely control the line speed of the winch. Advantages to adding a VFD to a winch system include:
• Increased electric power to output power efficiency ratio
• Easier starting on the electric motors, power can be slowly ramped up
• Less wear and tear on electrical and mechanical components
• Infinite range of customizable operator controls, joysticks, and automation
• Option of adding regenerative braking circuitry
• Automated and adjustable holdback tension in twin opposing winch systems

#### Regenerative Braking:

In addition to a VFD, regenerative braking circuitry can be installed to further increase the return of your new winch system. With regenerative braking, whenever the load is being slowed down and the winch is rotating faster than the input, the regenerative braking circuits put the excess current generated by the freewheeling motor back into the line. In systems where the load is continually being started and stopped, as occurs in barge positioning systems and most general winches and hoists, a large amount of energy savings can accumulate. The standard way of removing this excess current in the past was with dynamic braking resistors that effectively dissipated the current generated into heat that was vented into the atmosphere. With today’s technology we can recover this current easily and return it to the supply line. Even though the initial cost of installing regenerative braking may be slightly higher, the payback period is short.

There are several different types of gearing used in modern gearboxes, each with its own advantages and disadvantages. Choices of gearing include:
• External and Internal Spur Gearing
• Helical Gearing
• Worm Gearing
• Straight Bevel Gearing
• Spiral Bevel Gearing
• Planetary Gearing
• Cycloidal Gearing

#### Spur Gearing:

Spur gears are the most common and cheapest gearing components. They consist of one small and one large straight cut gear meshing with each other. They produce an amount of gear noise that at higher RPMs can become a nuisance.

#### Helical Gearing:

Helical gears are similar to spur gears except that instead of straight-cut teeth, the teeth are cut in a helix shape. This allows the gears to operate smoother, with less noise and vibration than spur gearing. A downside to helical gearing is the fact that the helix cut causes the gears to create a thrust force that must be opposed by thrust bearings.

#### Worm Gearing:

Worm gears consist of one large straight cut gear and one “worm” screw type gear meshing with the top of the straight gear. Operation of worm gears is similar to a typical screw. As the screw gear rotates it translates the motion 90 degrees through the straight cut gear. These gears are inefficient, but good at transmitting rotation at a right angle for a low cost.

#### Straight and Spiral Bevel Gearing:

Straight bevel gears have tapered conical teeth which intersect the same tooth geometry. Bevel gears are used to transmit motion between shafts with intersecting center lines. The intersecting angle is normally 90 deg but may be as high as 180 deg. When the mating gears are equal in size and the shafts are positioned at 90 degrees to each other, they are referred to as miter gears. The teeth of bevel gears can also be cut in a curved manner to produce spiral bevel gears, which produce smoother and quieter operation than straight cut bevels.

#### Planetary Gearing:

Planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which rotates relative to the sun gear. Planetary gearing systems also incorporate the use of an outer ring gear or annulus which meshes with the planet gears and is generally held fixed. Advantages of using planetary gears over typical parallel shaft gearing is a high power density in regards to the volume taken up by the gearing, along with a very high efficiency: 3-10% loss in one planetary reduction step as opposed to up to 30% loss in worm and spur gearing.

#### Cycloidal Gearing:

View Cycloidal Gearing Picture Cycloidal gearing is a relatively new method of gear reduction in which the input shaft drives an eccentric bearing that, in turn, drives a cycloidal disc in an eccentric cycloidal motion. The output shaft is connected to the cycloidal disc with several pins that the disc is free to rotate around.

The number of pins on the ring gear is larger than the number of pins on the cycloidal disc. This causes the cycloidal disc to rotate around the bearing faster than the input shaft is moving it around, giving an overall rotation in the direction opposing the rotation of the input shaft. The cycloidal disc has holes that are slightly larger than the output roller pins that go inside them. The output pins will move around in the holes to achieve steady rotation of the output shaft from the wobbling movement of the cycloidal disc. The reduction rate of the cycloidal drive is obtained from the following formula, where P means the number of the ring gear pins and L is the number of pins on the cycloidal disc.

Cycloidal gearing has many of the same advantages of planetary gears, with even higher efficiency, and an extremely high shock and overload capacity. When paired with spiral bevel gearing for a final gear reduction, the overall efficiency of the gearbox can be upwards of 94%. Cycloidal Gearing Picture