How to Calculate Sun Shade Sail Forces?

1,Determine the area of the solar sun shade sail. A good place to start would be a 1-square kilometer (10^6 square meter) sail.

2,Determine the reflectivity of the sun shade sails. A black, completely absorbent triangle sun shade sail would have a reflectivity of 0 percent, while a perfect reflector would have a reflectivity of 100 percent. For this example, take a reflectivity of 90 percent.

3,Determine the solar flux at the distance from the sun at which your sun shade sail canopy will operate. The solar flux is the energy density of sunlight. For this example, put your sail at the same distance from the sun as the Earth. The energy density there is about 1350 joules per square meter per second. To calculate for other distances from the sun, multiply 1350 times (distanceEarth’s orbital radius)^2.

4,Calculate the momentum of the sunlight at your chosen distance from the sun. The momentum is the energy divided by the speed of light. For this example, the momentum would be 1350 3.0 x 10^8 = 4.5 x 10^-6 kg-ms.

5,Calculate the force over the whole square sun shade sail. The force is equal to the momentum change. If the light is absorbed, then the momentum change is equal to the momentum of the photons calculated in the previous step times the area of the sail. If the light is reflected straight back, then the momentum change is equal to twice the momentum in the previous step. For situations in between, the force is equal to the momentum of the light times (1 + reflectivity), where the reflectivity was determined in Step 2.

So the force = 4.5 x 10^-6 10^6 (1 + 0.9) = 8.55 Newtons.