Dead Reckoning

Real Navigation – Dead Reckoning

Flying from point A to point B is easy in principle, if you just know where those points are. They are a certain distance apart and relative to each other in certain direction. So all you need to do is to fly from point A for the required amount of distance to the direction of point B.

A flight planner will gladly give the two important details, the direction and the distance, between two points. The trick is how to follow the plan, flying exactly the required distance to the required direction.

This navigating tactic is called dead reckoning (or ded reckoning, for deduced reckoning). It’s useful when you can’t navigate by pilotage, i.e. by landmarks and ground references. This is needed in particular over sea and deserts, or in bad weather. I’ve tried to minimize the need for dead reckoning so that it would only be assistive means of navigation, but I will make some desert crossing where it will be the primary navigation technique (as for the weather, I’ll try to avoid flying in low visibility).

Estimating

So, the estimating the distance covered is the easier of the two things to manage. It’s directly dependent on the speed of the aircraft, because as soon as we know the speed and time elapsed (which is easy to measure), we can calculate distance: distance = time x speed.

But there are a number of things to consider. First, this estimation works only with constant speed (or average speed). That means it’s actually not that easy to estimate the distance flown at X minutes after takeoff, because it takes some time to accelerate to constant cruise speed. However dead reckoning can be performed based on any ground reference fix, which doesn’t need to be the airport of departure. So, any fixed location along the way will do after establishing cruise speed.

Next, the speed indicated by instruments is not the speed flown over ground. Any head or tail wind will affect the actual ground speed, and must be accounted for. Also the higher you fly, the less dense the air is, meaning that the indicated air speed will be lower. There’s luckily a conversion formula from indicated airspeed to true airspeed, considering altitude (although it is dependent also on temperature, but to a lesser extent). Finally, the Hughes Racer displays speeds in miles per hour, while I use knots (nautical miles per hour) in navigation and flight planning.

Direction
The other thing to manage is the direction of flight.

In flight an aircraft always moves relative to air, not ground. Therefore any sideways wind will carry the aircraft to the left or right of the course it would otherwise travel above ground. Correction required in heading to compensate for the wind is proportional to the ratio of true airspeed and perpendicular wind speed. It is not easy to calculate it exactly, but a rough estimate is 60 x crosswind speed / true airspeed degrees into the wind, where crosswind speed can be calculated thus: take the direction difference of your track and wind direction, and think it as minutes (say, 20 degrees —> 20 minutes). Then consider what portion of an hour the resulting minutes amount is, and multiply that by the total wind speed. For example, 20 degrees wind from forward left at speed 15 knots will have 1/3 x 15 kn = 5 kn crosswind component. If flying at 200 knots, the heading correction for wind would be in the order of 60 x 5 kn / 200 kn = 1.5 degrees.

For wind correction, one must remember that wind direction is reported relative to true North, not magnetic (which is what the compass shows).

Magnetic declination must be applied also to any directions taken from a paper map. Luckily, the flight planner takes this into account, so headings are reported correctly in the flight plan. Of course the magnetic declination may change during a flight leg, but the difference will usually be insignificant (however, in Leg 9 from Victoria Falls to Windhoek there’s 6 degrees change in declination).

Lastly, it is possible that when following the great circle route—the shortest route between two points on Earth—the heading may change as the flight progresses. This also will not be a significant concern.

Conclusion

Despite all the above, the most important way of keeping track of actual heading and speed is to measure it using ground references. So, aiming to a distant ground reference directly ahead or a few degrees off, and observing how closely it passes, the crosswind factor can be assessed. Similarly, passing over two landmarks whose distance is known (from the map) and measuring elapsed time between them, actual ground speed can be measured. On a larger scale, tracking progress on map helps estimate progress for the remainder of flight as well.