Offtracking, and the two lengths that decide it
Put a truck and trailer into a sustained turn and the trailer wheels do not follow the truck wheels. They cut inside, and once the rig has settled into the curve the amount is fixed by geometry alone: not by speed, not by steering input, not by the driver.
The steady-state result is that each towed unit tracks on a radius equal to the square root of the previous unit radius squared minus its own length squared. Chain it for a truck and one trailer and the trailer axle path radius is the square root of the front axle path radius squared, minus the wheelbase squared, minus the trailer hitch-to-axle length squared, plus the hitch offset squared if the hitch sits behind the drive axle.
Work the default numbers. A 50 ft outside radius on an 8.5 ft wide rig puts the front axle on 45.75 ft. Square that and you get 2,093. Take off 13.5 squared, which is 182, and 20 squared, which is 400, and add back 4 squared, which is 16. That leaves 1,527, whose root is 39.07 ft. The trailer axle is running 6.68 ft inside the front axle, and the inner edge of the trailer is another 4.25 ft inside that, at 34.82 ft. The rig is using 15.18 ft of width to get round a turn it could walk around in eight and a half.
Lengths add in quadrature
This is the counterintuitive part and it is worth internalising. The wheelbase and the trailer length do not add up; their squares do. A 13.5 ft wheelbase with a 20 ft trailer gives a governing length of the square root of 182 plus 400, which is 24.1 ft — not 33.5.
| Change | Governing length | Offtracking at 50 ft outside radius |
|---|---|---|
| 13.5 ft wheelbase, 20 ft trailer | 24.13 ft | 6.68 ft |
| 13.5 ft wheelbase, 24 ft trailer | 27.54 ft | 9.00 ft |
| 11 ft wheelbase, 20 ft trailer | 22.83 ft | 5.90 ft |
| 13.5 ft wheelbase, 20 ft trailer, gooseneck over the axle | 24.13 ft | 6.88 ft |
Because the squares dominate, adding four feet to an already long trailer costs more than taking two and a half feet off the wheelbase saves. It also explains why a gooseneck, which puts the kingpin over the drive axle instead of four feet behind it, offtracks slightly more than a bumper pull of the same hitch-to-axle length: the hitch offset term that pulls the figure back disappears.
Sizing a turnaround
The useful question is usually the reverse of the one above: given something in the middle of the turn, how much room does the whole thing need? Rearranging gives a closed answer. Take the obstacle radius plus half the rig width, square it, add the wheelbase squared and the trailer length squared, subtract the hitch offset squared, take the root, and add half the width again. That is the outside radius required.
For the defaults — a 15 ft obstacle, 8.5 ft wide rig, 13.5 ft wheelbase, 20 ft trailer, 4 ft hitch offset — that comes to 34.86 ft, so the turnaround needs about 69.7 ft of clear diameter. Take the island out entirely and it drops to 28.42 ft radius, 56.8 ft across. Put a 24 ft trailer on instead and the 15 ft island version rises to 37.61 ft radius, 75.2 ft across. Those are the numbers that decide where a fence line goes.
Steady state is the worst case, and a corner is not steady state
Everything above assumes the rig has been in the same curve long enough to settle. It has not, on a normal ninety degree corner: the trailer is still cutting in when the truck is already straightening out, so the actual offtracking through a short corner is less than the steady figure. On a full turnaround, a loop, or a long sweeping bend, it is the right number.
What the geometry also cannot tell you is what happens in reverse, which is where most trailer damage on a property occurs, or what a driver does when a turn is marginal. It says nothing about surface, about whether the ground carries the load, or about grade — a turn on a slope behaves differently from one on the flat. For getting off a public road into an entrance, the driveway apron turning radius calculator handles a single vehicle swinging in and the apron it needs, and the gate setback and stacking calculator covers how far back a gate has to sit so a rig is clear of the road while it waits. Parking several vehicles rather than turning one is the driveway parking layout calculator.
Questions people ask
How much does a trailer cut inside the tow vehicle in a turn?
On a sustained turn, the trailer axle runs on a radius equal to the square root of the front axle path radius squared minus the wheelbase squared minus the hitch-to-axle length squared, plus the hitch offset squared. For a 13.5 ft wheelbase with a 20 ft trailer and a 4 ft hitch offset on a 50 ft outside radius, that is 6.68 ft of offtracking, and the swept path from the outer edge to the inner edge is 15.18 ft. Tighter turns make it worse quickly: the same rig at a 35 ft outside radius offtracks over ten feet.
How big does a turnaround need to be for a truck and trailer?
With nothing in the middle, the constraint is just that the geometry closes: the outside radius has to exceed the root of the wheelbase squared plus the trailer length squared minus the hitch offset squared, plus half the width, which for the default rig is 28.05 ft, or 56.1 ft across. With something in the middle to clear, add the obstacle. A 15 ft island pushes the required outside radius to 34.86 ft, so about 70 ft of clear diameter. Those figures are the geometry only — surface, grade, drainage and where the driver can actually see are separate.
Does a gooseneck offtrack more or less than a bumper pull?
For the same hitch-to-axle length, slightly more, which surprises people. A bumper pull hitch sits behind the drive axle, and that rear offset adds a term back into the expression that reduces the offtracking a little. A gooseneck kingpin sitting over the axle has no such offset. In practice goosenecks usually still handle better in a tight yard, because they are more stable in reverse and because the hitch-to-axle length of a gooseneck is measured from a point further forward on the truck, but the pure steady-state offtracking for identical lengths favours the bumper pull by a few inches.
Why does the calculator sometimes say the turn does not close?
Because the expression under the square root goes negative, which means no steady circular path exists for the whole rig at that radius. Physically it corresponds to the trailer being asked to track through or past the centre of the turn, which it cannot do while moving forward. That is the boundary where a turn stops being driven and starts being shunted — pull forward, back up, pull forward again. The output prints the smallest outside radius at which the geometry does close for your rig, which is the honest minimum for a one-shot turn.
Is the swept path the same going forward and reversing?
No, and reversing is not modelled here at all. Backing a trailer is an unstable process rather than a geometric one: the trailer amplifies steering input instead of damping it, the path depends on the driver correcting continuously, and the swept area can be much wider than the forward figure or much narrower depending on how it is done. Everything on this page describes forward motion in a settled curve. Sizing a yard so that a rig can be driven round rather than reversed is usually the point of doing the calculation in the first place.