Is there a mechanical engineer in the house?!?
Actually, there is. :dance:
Here is a pic of a generic mast with mast raising system. The extra lines with the little box on the end represent the perpendicular distance between that piece of rigging (hoist or halyard) and the hinge. It's theoretical, as there is no actual structure there, but you can generally eyeball it with a tape measure by swinging an arc with the tip of the tape on the hinge bolt and finding the shortest distance to the halyard or to the center of the system of ropes in the case of the hoist. I left the little 'square' indicating box off a couple of them by accident, but it's a pain to edit, then created jpgs, then upload, so I left them as-is.
Variables are as follows:
Wmast - mast weight, taken at the center of gravity
MAmast - moment arm of the mast about the hinge
MAhoist - moment arm of the mast raising hoist about the hinge
MAhalyard - moment arm of the jib halyard about the hinge
The total tension force in the hoisting system is easily calculated by summing moments about the mast hinge, and setting it equal to zero (static equilibrium).
M = 0 = Wmast*MAmast - Fhoist*MAhoist where Fhoist is the tension force in the hoisting system
Using made up numbers below of 100 lb for the mast weight at 120" from the hinge, and locating the hinge (tabernacle) and hoist termination at arbitrary locations that look reasonable to my eye for a typical boat, and using a 5 ft gin pole as an example, you get
0 = 100 lb * 120 in - Fhoist * 35 in, or 100 lb*120 in / 35 in = 343 lb tension load in the hoist (total, regardless of the number of parts).
With the mast at about 20 deg. off the horizontal, the perpendicular distance from the hinge to the hoist has increased, so the moment arm is longer. The gin pole, mast, and halyard geometry hasn't (and won't) changed at all, but the horizontal distance from the CG to the hinge has decreased. The moment at the hinge from the mast has decreased, and the moment arm to the hoist has increased (longer theoretical lever arm), making for better mechanical advantage and somewhat easier lifting, though not hugely so (yet).
I get about 292 lb in the hoist at this position.
With the mast up around 60 degrees or so, the moment about the hinge from the mast weight has gotten pretty small, and the moment arm for the hoist is almost at its largest.
I get about 100 lb in the hoist. Obviously, as the mast is raised, the mast weight moment at the hinge decreases to zero (at vertical), while the hoist geometry, which has already gotten favorable, only improves further as the gin pole to hoist rope angle approaches perpendicular (can't get any better than that).
Anyone can calculate this by simply measuring the perpendicular distance from the hinge to the hoist rigging with a tape measure (with the rigging taught), and the horizontal distance to the mast CG (since gravity always acts downward). The mast weight and CG location has to be known, though the CG is probably pretty close to the center for a mast of constant section with little other stuff on it.
I'll post some diagrams of the halyard termination question shortly. I have to do an errand with the Admiral. :neutral: