Can planes generate enough force to displace cloud, such that the displacement is visible from the ground? Is it possible for planes (helicopters, jets, commercial airplanes, etc) to generate enough force to displace any amount of cloud, such that the displacement is visible from the ground?
Assuming an observer is standing on the ground, and viewing clouds in the sky. 
Can anyone comment on whether it is possible for any planes (as above) to generate enough force to move an amount of cloud such that the movement is visible from the ground?
I'm assuming clouds can be moved, as I've often seen winds that blows clouds a certain distance.
 A: A plane is a very dense object, compared to air. If you can see a plane, you can certainly see enough of a cloud to support it. So it is definitely true that you can see a cloud moved by a plane. Here's a photo:

Can you see that from the ground? Sure you can, from those hills in the background. If you can see the plane, you can see the cloud that's holding it up.
A: The density of clouds is only slightly greater than the density of air (obviously, otherwise the clouds would sink :-). The water content in a cloud ranges from 0.1g/m$^3$ to 5g/m$^3$. Given that the density of dry air is 1.28kg/m$^3$ the water only adds 0.5% to the density at most.
So when you ask if a plane can move a cloud, you're effectively asking if a plane can move air enough to be visible from the ground. Planes can certainly move a lot of air as this scientific experiment shows. However from a distance of a few miles a plane is pretty small, and so is the amount of air it moves. Whether this is visible from the ground depends on how you define "visible", but I think most people would say the wind caused by a plane is small compared to the winds that occur naturally. Unless you're using binoculars you're unlikely to see clouds moving much because of a plane.
A: When wind moves clouds, the whole mass of air is moving and clouds (the water droplets) are moving with it. On the other hand airplanes try to be as stremlined as possible and minimize the drag to be more efficient. Planes of course cause some disturbance in the cloud, but with most clouds I would say that the amount is so small that it can't be detected, not at least with naked eye.
As pointed out in the comment, fog is a cloud that is just located on the ground level. That means you can study how clouds behave on ground level, at least with slower moving objects.
If you just want to detect the planes, then using radar or maybe detecting the warmth of the engines is quite a lot more efficient.
