An approximation procedure is described, which greatly simplifies dead reckoning on a tortuous path. The journey is divided into N segments of equal length, L. The overall direction is approximately the average direction of the segments. The net distance is approximately NL[1-var(α)/2], where var(α) is the variance (in radians squared) of bearings, αi, corresponding to the segments, and must be less than 0·7. Propagation of random errors is discussed. In a case study in sub-tropical rainforest the technique gives an estimated position whose associated circle of 68% confidence has a radius of about 10% of the net distance.