You are right that a free-spinning dyno roller, in a world without tire friction or roller inertia, will not produce any fore-and-aft force on the car.
However, the entire point of a dyno is that the rollers don’t spin freely: they exist for the purpose of absorbing power from the vehicle’s driveline (to simulate vehicle inertia during acceleration, or drag during cruise) or delivering power to it (to simulate a downhill run or a braking event). Assuming the dyno is in absorption mode (e.g. to simulate the aero drag of a highway cruise or the inertia of the vehicle during an acceleration event), the vehicle must apply tractive force from its tires to the rollers to keep the rollers spinning (or accelerate them). To prevent the vehicle from accelerating forward, there must be something applying an equal-and-opposite force; that something (depending on who’s telling the story) is the horizontal chain attached to the bumper, or the stabilizing roller (if there is one) that forms a cradle with the main power absorption roller, or some combination of the two.
Unlike the plane-on-a-treadmill nonsense, this is not a hypothetical situation. Motorcycle dynos really do have modest attachments, since bikes can at most deliver maybe 1000 pounds of tractive force. Passenger car dynos really do have larger attachments, and heavy duty truck chassis dynos really do have bloody massive attachments, since they can deliver tens of thousands of pounds of tractive force.
Some pictures to illustrate how vehicles are secured on real chassis dynamometers.
A passenger car with rear hold-down straps. Upthread Nefario mentioned the use of hold-downs to provide downforce that gives the tires a better grip on the dyno roller. This may be a necessity for max-power testing (e.g. for racing development), but for emissions and fuel economy testing it’s a no-no, since the increased downforce also increases rolling resistance beyond what is encountered on the open road. For these tests, your restraints can’t apply vertical load to the chassis, only horizontal load; you can do this with horizontal chains or straps attached to the chassis, or you can anchor the non-drive wheels (if any) to the floor. Obviously if you have an all-wheel-drive vehicle being tested, you need an all-wheel-drive chassis dyno, and your only choice of restraints then is horizontal members affixed to the chassis.
A heavy-duty truck cab on a chassis dyno, with horizontal chains providing restraint. The chains are crossed laterally to prevent the chassis from wandering left and right on the rolls. In this particular image, the tongue weight of the trailer is simulated by a hydraulically (or possibly pneumatically) loaded beam across the fifth-wheel; this way they don’t need to have floor space to accommodate a 53’ trailer (or load/unload tens of thousands of pounds of ballast). At the front of the truck cab you can just make out the pink chains used to restrain the vehicle during braking events.
Another truck on a chassis dyno, this time showing the front chains that prevent the truck from accelerating to the rear during braking events. Again the chains are crossed to better resist lateral movement of the chassis.
There are two types of dynamometers, inertial and brake. The rollers DO spin freely in an inertial dynamometer. Think of pushing (accelerating) a heavy cart; are you exerting a force? That’s most of the force on the chains; The other force vector is pulling the car down to get traction on the heavy roller. The car is “dynoed” by accelerating and the rate of acceleration of the roller can be translated to an instantaneous torque at a given speed from which power may be calculated.
The brake dynamometer is the steady-speed design with the car tires working against a braking device on a roller to measure applied torque. Torque + Speed ==> Power
Both designs use chains for the same reasons and have the same chain tension at a given torque-speed condition.
Do you believe that instantaneous torque at a given RPM really means anything? It’s a way to compare two cars or before/after modifications. But real engine developers use brake dynomometers so they can hold loads long enough to understand tuning in a steady state.
