The physics concepts involved in a luge run are fairly basic:
force and inertia - A great amount of force is required to get the slider moving at the start of the course.
gravity - The force of gravity pulls the slider and the sled down the track.
friction - The amount of friction between the sled and the track works against gravity and is a prime determining factor in speed.
aerodynamic drag: Aerodynamic drag acts on the slider/sled combination to resist its motion through the air. The lower the drag, the higher the speed.
g-force: A g is equal to the force exerted by gravity. It is the force acting on a body that is accelerating. If a slider is facing 3 g's through a turn, his body feels three times heavier than his actual weight when he is at rest.
At the start of the course, the slider/sled unit is at rest. The slider's goal is to begin the run with the utmost speed, so he needs to propel the racing unit onto the course with as much force as possible to overcome its inertia (its desire to remain at rest). If the slider weighs 198 pounds (89 kg), and the sled weighs 50.6 pounds (23 kg), that's a combined mass of about 247 pounds (112 kg). By rocking back and forth at the top of the track, the slider needs to generate enough momentum to propel 247 pounds through the first 10 feet of the course in something like 2 seconds to achieve a really good start.
There are two people on this sled, meaning an extremely tight fit to minimize form drag.
As the slope begins, the slider lies down on the sled and lets gravity take over. In luge, higher weight means greater speed. The greater the weight of the athlete, the greater the force of gravity pulling her down the track. One of the forces standing in the way of gravity is friction. To reduce the amount of friction between the sled and the track, the steels are polished with numerous substances, including sandpaper and diamond paste.
Another force acting against the pull of gravity throughout the run is aerodynamic drag. Aerodynamic drag consists of air friction and form drag. In luge, when air runs over the top of the rider, it interacts with the materials of the helmet and racing suit. This results in air friction. To reduce air friction, racing suits are slippery and skin-tight, and the visor on a luge helmet is rounded and extends all the way under the slider's chin so there are no air pockets. The interaction between the air and the frontal shape of the slider/sled combination results in form drag. In addition to using the most aerodynamic shapes for the sleds, the slider tries to further minimize form drag by maintaining an aerodynamic body position. The less area he presents to the oncoming air, the better. Lifting the head an inch so the slider can better see the track increases form drag and can add several thousandths of a second to the run time. In doubles luge, the taller athlete lies in front, between his partner's legs, to achieve a smoother profile. Many sliders spend hours training in wind tunnels to find the ideal body position to minimize drag.
Probably the most physically battering points on a luge run are the turns, and especially the turn combinations, when g-forces increase. Acceleration and deceleration throughout a luge course puts an average force of up to 3 g's on a slider's body. Forces can reach up to 5 g's in banked turns, when centrifugal force* adds another dimension to the forces acting on the slider.
Centrifugal force pulls the slider outward in the turn. To maintain speed, the slider must perfectly balance the centrifugal force with the force of gravity pulling him downward through the course. This means finding the "sweet spot" and staying there. If the forces are balanced, the sled will smoothly move through each turn and back into the straightaways. If they are unbalanced, the slider will have to steer too much, slowing down the run.