in cycling, team follow cars are required to maintain a minimum distance from their riders during time trials for this very reason (although i imagine the effects in that context are much smaller and dependent on the conditions, esp the wind speed, direction, and strength). FYFD, is there a simple way to understand where this upstream influence comes from? or a specific term in the navier-stokes equations that it results from?
Cars following riders during a time trial can actually make a huge difference! One study from a couple of years ago estimated that a car following a rider in a short (13.8 km) time trial could take 6 seconds off the rider’s time. The images up top show a simulation from that study with a car following at 5 meters versus 10 meters. The colors indicate the pressure field around the car and rider. Red is high pressure, blue is low pressure. Both the car and the rider have high pressure in front of them; you can think of this as a result of them pushing the air in front of them.
A large part of the rider’s drag comes from the difference in pressure ahead and behind them. (For a look at flow around a cyclist that focuses on velocity instead, check out my video on cycling aerodynamics.) When a car drives close behind a cyclist, it’s essentially pushing air ahead of it and into the cyclist’s wake. This actually reduces the difference in pressure between the cyclist’s front and back sides, thereby reducing his drag. Because cars are large, they have an oversized effect in this regard, but having a motorbike or another rider nearby also helps the lead cyclist aerodynamically.