Question

Problem 4

Sometimes it is useful to investigate old technology to see if it can be useful in changing times.

Clockwork car: pre-1895

The vehicle was driven by four large springs, presumably of the clock type, mounted inside what appears to be a cylindrical housing at the rear. It could go three miles on one winding, but just how much effort was required for that winding is not currently known.

http://www.douglas-self.com/MUSEUM/POWER/clockwork/clockwork.htm

Is the concept of wind-up “cars” feasible? Let us investigate the idea. Initially we need to do a proof-of-concept calculation to answer the question “What are the characteristics of the springs that could do such a thing?”.

We know the amount of energy a spring stores U = ½kx² and we know the maximum force that needs to be applied is F=kx. So the unknowns are ‘k’ and ‘x’.

Let us assume that a person can apply a force (F) equal to their body weight to wind up the spring and that by some clever ratcheting and using large coiled power springs each spring can be wound up a considerable distance (x). Would we have enough energy to power the car?

What is that energy needed for? Initially it is needed to get the car up to speed then to maintain that speed over a distance of 3 miles. Let us choose a speed that is around walking speed. I know from old news reals this was the case because sometimes they had a person walking in-front of the cars waving a red flag to warn people to get out of the way. Assume we can ignore the initial energy to get the car started because we can have someone give the car a push.

Therefore it is only the drag force and rolling friction that have to be taken into account. Rolling friction is difficult so let us work with the drag force first.

Drag force R = ½DrAv² if we assume D=0.5, A = 1m² v = 1.23m/s

http://en.wikipedia.org/wiki/Drag_coefficient

http://en.wikipedia.org/wiki/Walking_speed

Then R = 0.5N

So the energy needed to go 3 miles is force x distance = 2191 J

Each spring therefore needs to store 548 J

So find the spring constant of the springs and how much they need to be wound up in order to store enough energy to overcome the drag force on a 3 mile ride.

Assess your answer, in the light of the assumptions that have been made, to see if it makes sense. Then decide if this old clockwork technology could be useful “new” technology. Give reasons for your answer.

Answer 1

Solution:

As the total drag force is 0.5 N, so 4 springs have to aplly atleast 0.5 N on the car to move.

As the spring force is kx, so kx should be equal to 0.5/4.

So,

Ans total energy stored by each string =

Solving equations 1 and 2,

we get x = 8768 metre = 8.78 km

    And k = 1.42X10^-5 N/M

So, we need a spring with a very low spring constant, but we will have to wrap a length which is more than the covered distance, in fact more than double the distance.

So, it is possible to have these kind of cars, but for larger distances very long springs would be required and wrapping of the very long springs will be very tediuos job and require a lot of work too.