When you stand on the ground the ground will exert a vertical force (W) on you that just balances your weight as shown in Figure 1. This force is often called the normal reaction. It is possible to stand on a surface where there is virtually no friction such as ice on a skating rink.
However once you try to walk or run some friction is essential as you can see from Figure 2. The vertical force is now G, this is a bit less than W for a reason that will be explained later and the frictional force is shown as F. This frictional force acts in the opposite direction to the horizontal component of the force of your foot on the ground. That means when your foot is ‘pushing forward’ at the start of a stride (Figure 2(a)) the frictional force acts backwards to prevent you slipping while when you are ‘pushing backwards’ at the end of the stride it acts forwards (Figure 2(c)).
The frictional force is related to the vertical force by the equation F = μG where μ is the coefficient of friction between your foot (or shoes) and the surface that you are walking on. This is usually between 0.6 and 0.75 for shoes and the floor. Remember that μ depends on both surfaces – the soles of your shoes AND the surface of the floor.
The resultant force (R) in each part of the stride is calculated using: R2 = G2 + F2
When you run your speed increases and you achieve this by increasing the length of your stride and the frequency of the movement of your legs. Both legs rotate as you run and the centre of gravity of your body also moves up and down by a few cm during each stride in both walking and running.
The reason that the vertical forces are greater in walking and running than they are when you are standing still is that in standing the vertical force has just to balance your weight. However in walking, and to a more extreme case in running, the force has to support your weight and produce a change of momentum as you land, changing the downward motion to an upward motion for the following stride. In walking this force would be up to 1.5 times your body weight while in running it might increase to between 2.0 and 2.9 times your body weight!
Wearing ‘good’ shoes with soles and heels that will absorb some of this shock is vital particularly for athletes who run long distances on hard roads.