Pulling an Airplane
Force required to pull an air plane.
The force to move an airplane on an absolute flat runway with no wind at constant low speed is equal to the rolling resistance between the plane and the tarmac.
The rolling resistance for the air plane can be calculated as
F_{r} = c m_{r} a_{g} (1)
where
F_{r }= rolling resistance (N, lb_{f})
c = rolling resistance coefficient
m_{r} = rolling mass (kg, lb_{m})
a_{g} = acceleration of gravity (9.81 m/s^{2})
Example  Force required to pull an airplane at constant low speed on tarmac
If the mass of a plane is 40000 kg and the rolling coefficient between the aircraft wheel and the tarmac is 0.02  the force required to overcome the rolling resistance can be calculated as
F_{r} = 0.02 (40000 kg) (9.81 m/s^{2})
= 7848 N
This force can be delivered by a pulling truck or  as occasionally seen  by a number of pulling people. Enough weight for the pullers are required to create friction forces against the tarmac that equals the plane rolling resistance.
The friction force for the puller can be calculated to
F_{f} = μ W
= μ m_{f} a_{g} (2)
where
F_{f} = frictional force (N, lb)
μ = friction coefficient
W = weight (N, lb_{f})
m_{f} = friction mass (kg)
Example  Required Mass for Pulling Truck
The friction coefficient between a pulling truck rubber wheels and dry tarmac is 0.9. Since pulling trucks are connected to air crafts nose wheels close to tarmac we simplify the calculation of required truck mass to
m_{f} = (7848 N) / (0.9 (9.81 m/s^{2}))
= 889 kg
Example  Air Craft Pulled by People
When persons participates in aircraft pulling there is normally an offset between the rope connected to the air craft nose wheel and the tarmac. It is common for persons to bend over with the rope over the shoulder or holding it in the hands.
The horizontal friction force between the persons shoes and the tarmac must be equal or larger than the air plane rolling resistance. The minimum required vertical force  or minimum weight of the people  depends on the bending angle as illustrated in the vector diagram below.
If they bend over 45^{o}  the vertical force or weight equals to the horizontal force. With rubber shoes and the same friction coefficient as above for the truck the weight of the people should be 889 kg. With an average weight of 80 kg/person  the number of persons can be calculated to
n = (889 kg) / (80 kg/person)
= 11.1
= 12
With a more realistic bending angle 60^{o}  the minimum vertical force or weight can be calculated as
W = tan(60^{o}) (7848 N)
= 13593 N
The minimum mass of people to achieve this weight can be calculated as
m_{f} = W / a_{g}
= (13593 N) / (9.81 m/s^{2})
= 1386 kg
With an average weight of 80 kg/person  the minimum number of persons can be calculated to
n = (1386 kg) (80 kg/person)
= 17.3
= 18
Related Topics

Dynamics
Motion  velocity and acceleration, forces and torque.