Not quite specific enough
A question that was asked at another forum that I thought I might get a straight answer (and explanation) for here:
If you have two identical semi trucks driving down the road.
One has no load. One has a very heavy load.
Will the heavy load displace more air than the truck with no load?
IMO these sorts of gross generalization questions are better unasked than answered. Sorry (sort of) to be pedantic, but the "right" answer depends on details the question doesn't provide...
What do you mean by "identical semi trucks driving down the road"? Do you mean vehicles of identical, typical semi-tractor-trailer construction traveling however they each travel under their particular conditions of load and environment? The typical rig is far from streamlined, especially at the rear. As the vehicles move through the air, vortices will be shed alternately from each side and impose cyclic forces that would tend to rock the trailer from side to side (top and bottom too, for that matter). Whether and how much that causes the rig to roll, yaw, and pitch as it travels will depend on the details of the supension as well as on the particular amount and placement of load. There's not enough specification in the query to determine whether the heavier or lighter rig will wobble more and sweep a larger volume; my
expectation, however, is that the suspension will be designed to ride more stably when bearing its design load than when unloaded.
Or do you also mean the details of the vehicles' motions are identical in every respect? Depending what you mean by "displace", that would reduce problem to the almost trivial determination of which vehicle is volumetrically larger or projects the most area in the direction of motion. The loaded rig will be volumetrically slightly smaller than the unloaded rig due to elastic compression of its structural members and compression of the air in its tires, though those effects will be on the order of parts per million. The greater effect will probably be a combination of shock-absorber piston travel and leaf-spring deformation lowering the trailer to present a smaller area in the direction of travel. That might be a few inches difference between empty and fully loaded... but the bottom of the tractor must lower the same amount as the top of the front of the trailer, so the net reduction is only the amount by which the tractor's wheels are withdrawn into the fender wells.
What's the "load"? Is it
in the truck , something like a really really fat driver or cargo inside an enclosed trailer? Is it
on the truck, like cargo sitting atop flatbed trailer? If it's
on the truck, does air "displaced by the load" count? Is it some idealized load force acting on the vehicle but not considered as a separate physical entity for purposes of this problem?
How is the load distributed on the vehicle; where is its center of gravity, what are its moments of inertia? These details matter how applied load changes the projected area of the vehicle, and they're probably
very important to the vehicles' roll/pitch/yaw/bounce behavior if we don't constrain them to motion
identical in all respects.
How much is enough to be considered "more"?
What do you mean by "displace... air"? The space that would be occupied by air but for the vehicle and its cargo? In that case motion doesn't come into play (relativistic effects aside
). The loaded
vehicle displaces less air because its structural members, shocks, and tire air are compressed to bear the load, but the effect is only a few parts per million. If the load is "real" and either external or we consider its displacement of air from the interior of the trailer, the
vehicle+load displaces more air, dominated by the density of the load itself.
Do you mean the volume swept by the moving vehicle's bounding surfaces over corresponding intervals of time? The total mass of air disturbed by the vehicles' passage at a particular speed through particular environmental conditions (and what counts as "disturbed")? Again, this depends strongly on whether we permit the vehicles to move "appropriately" for their load or constrain them to motion identical in detail; the former is unknowable in the general case, and the latter is hardly worth knowing (IMO).
We've even got problems if we try to guess the "spirit" of the assertion, which might be something along the lines of whether the loaded or unloaded truck is more fuel-efficient. I'd be very surprised if the loaded truck went as far on a given charge of fuel, but it's certainly more efficient in terms of delivering payload rather than just truck.
OK, so I rant a bit
