Lift and drag forces both can be used across your sail to provide propulsion.


Assuming no vertical angle-of-attack $\alpha$ (won't assume that in bit), the profile of your sail providing force perpendicular to the surface (per mast) is twice the sail diameter high and the full width of the sail wide.
$A \approx 2Dw$
The total amount of canvas is $A = \pi Dw \approx 3Dw$.
You learn something interesting from just this. In this configuration, you've lost roughly a third (33%) of your canvas available for thrusting.
What have you gained?
By the same reasoning, roughly two-thirds of the canvas air is now available for lifting.
The equation for lift is:
$L = {1 \over 2} C_L \rho_{air} (v_{air} - v_{ship})^2 A$
The density of air ($\rho_{air}$) is 1.1 ${kg} \over {m^3}$, and the lift coefficient ($C_L$) of a sail can be up to 1.4 (see chart below). So, the equation above becomes.
$L = (0.5) (1.4) (1.1) (v_{air} - v_{ship})^2 A = 0.77 v^2 A$
For a ship like a Caravel with about 100 square meters of canvas, A becomes about 66 square meters and the equation simplifies a little further to -
$L = (0.5) (1.4) (1.1) (v_{air} - v_{ship})^2 66 \approx 50 v^2$
Thrust from lift, neglecting using drag for thrust, is the same
$T = (0.5) (1.4) (1.1) (v_{air} - v_{ship})^2 66 \approx 50 v^2$
Drag, the force countering thrust to slow the boat, comes from skin friction and displacement. In a Caravel shaped boat, mostly displacement.
$D = {1 \over 2} \rho_{sea} v_{ship}^2 A_{profile}$
Where the density of sea water is 1,200 ${kg} \over {m^3}$ and the boat profile is the width (2 meters for a Caravel) times displacement (also 2 meters for the Caravel), and the equation above becomes-
$D = {1 \over 2} 1,200 v_{ship}^2 4 = 600 v_{ship}^2 4 = 2,400 v_{ship}^2$

Let's try this out at a few speeds
In leisurely 15 knot ($\approx 7.5 {{m}\over{s}}$) winds, $L \approx 50 v^2 \times 2 masts$, you get about 5,600 Newtons of lift per mast. That'd offset the weight force of about 560 kilograms. And, for a 50 ton ship, isn't really significant.
Might be good to work out cruising speed and compare it to a ship with flat sails.
At cruising speed, the thrust being generated by the wind is being totally balanced by drag force (so that the ship is neither accelerating nor slowing) $T = D$
For our ship $T = 50 (v_{air} - v_{ship})^2 \times 2 masts; D = 2,400 v_{ship}^2$
I don't have any way other than trial-and-error to solve for that, so maybe take it with a grain of salt that your cruising at 1.2 $m over s$, or about 2 knots.
A Caravel, our reference ship, would be travelling in the same winds at $T = 77 (v_{air} - v_{ship})^2 \times 2 masts; D = 2,400 v_{ship}^2$ at about 3 knots (or 50% faster)
Things start to get interesting in high wind
With a strong 45 knot wind (22.5 m/s), things start to become interesting.
$L = 50 v^2$ \times 2 masts$ = 50,000 Newtons. Or, 5 metric tons of weight. For a 50 ton ship, it's about 10%.
The drag of the boat hull is based on it's width (2 meters) multiplied by how deep it's sitting in the water (also 2 meters). The tonnage of the boat is the displaced 1,200 kg/m^3 sea water = 2 x 2 x 10 x 1,200 ~ 48,000 kg.
Lift, pulling some of the weight off the boat, means the boat will sit higher in the water. About 10% (0.2 meter) higher in this case.
This has 2 benefits :
- Can sail in shallower water
- Can move faster
In this particular case, being 10% higher in the water increases speed by about 5%. We're closing on the performance gap with the comparison ship : 8 knots (us) vs 9 knots (comparison).
What about dangerous conditions?
At 60 knot winds (30 m/s), the boat is 10% (0.5 meters) higher and still a little slower than the comparison ship (11 knots vs 12)
How about a lighter ship?
As you can see, lift vs. weight is how this effect scales. Decreasing both our reference ship and ship's tonnage by half to 25 tons, the cylindrical sail finally starts to outperform it's competitor. The ship sits much higher in the water at 60 knots winds (0.6 meters total displacement) meaning invisible coastal shoals are much less of a threat. It also sails faster: almost 19 knots in these conditions, vs the competitor at 16 knots.
Going further
Modern competition boats, I read, are about 6 to 12 tons. In this case, it seems, you're nearly on top of the water and much faster than the competition at 30 knots vs 26.
Lift is getting cut as the relative wind ($v_{air} - v_{ship}$) decreases with increasing boat speed. Would need to re-formulate how lift works to really explore this area.
I think there are other questions about stability and how to control the thing, but it seems like a very interesting concept!