Surveying without instruments

Warwick Rowell, Monday 24 February 2014

In the early 1990s, two surveyors who were doing a Permaculture Certificate course with me were blown away when I said “Of course as a Permaculture designer you can do 95% of the surveying you need without a surveyor and without instruments.” I have confirmed the truth of this comment many times, and probably taught about a hundred people how to do it, but this is the first time I have written it up. Your comments and elaborations and any other “quick and dirty” methods you know would be appreciated; if you send them to me, I will collate them, and write a follow up article.

Okay. Here we go.

Firstly, you need a known, fairly long distance. 50m would be minimal, 200m would be more than enough. Then you walk up and down several times, at your normal walking pace, and count the number of paces you take, and average them. Then you can build a mental or written table for how many paces you need for various distances at say 10m intervals. I’m very lucky; it takes me 110 paces to walk 100m under a wide variety of conditions, so every 11 paces is 10m, and so on. I can usually get within 1-2% accuracy for most distances. Occasionally I have to make an allowance for very rough ground, or very steep slopes, either up or down, but you get a good feel for the need for this after a while.

For reasonably accurate diagrams of what you are pacing out, you can use your body as a ruler. The width of my little finger nail is 1cm. The width of my index finger is 2cms. The top joint of my thumb is 3cm. The length of my index finger is 10cm. The span of my thumb to index finger is 20cm. The span from my thumb to my little finger is 250cms. When I have my boots on my belly button is 1m off the ground. My chin is.., the tip of my nose is… Importantly my eyes are 162cms off the ground (with my feet spread one foot apart) – so when I sight for a level I know that I must allow for that height.

Now the most interesting bit; how to measure angles accurately to within one degree. If you have a known right angle, you’re better off, but if you don’t, rely on your body sense; just get your back along a straight wall or fence, spread your hands wide at shoulder height, and bring your hands together in front of you. With both eyes open, identify a spot on the horizon between your thumbs. This will be so close to 90 degrees from the wall as doesn’t matter. Now extend your dominant arm at eye height, clench (for most people) your right fist, and turn your wrist so your knuckles are horizontal. Line up the base of the knuckle of your index finger with whatever it was you identified at the left hand side of your right angle. Now carefully, without moving your hand at all, or your head more than necessary, identify a point on the horizon that lines up with the base of the knuckle of your little finger. A complex outdoor horizon helps here. Move your fist to the right, still at arms length, so the point you selected is now aligned with your index finger knuckle, count two, and identify a new point behind your little finger knuckle. Repeat this, counting as you go, until you get to the right hand side of your ninety degree mark. Do this several times, to get comfortable with it, and to get a good feel for the number of fists you take to cover ninety degrees.

The next step is to do some simple maths. I had ten fists for ninety degrees, so my fist covers nine degrees. Eleven fists would be eight degrees, nine fists would be ten degrees, and so on. Now you need to work out the finer divisions. For most people, the knuckles of your index and middle fingers are larger than those of your ring and little fingers. My ring and little finger knuckles are four degrees wide (approximately); so each is two degrees wide, so the angular distance between the valley between my ring and little fingers, and the peak of the knuckle of either is one degree. You will need to work this bit out for yourself, and your fist, and find what is the most accurate and easy to remember.

Once you have done this, you have a remarkably accurate means of assessing angles either horizontally or vertically, to within about half a degree of accuracy. I have used both vertical angles and horizontal angles to position houses for winter sun access over a tree line (with a diagram of how sun angles change with time and date). With the same chart you can work out when winter sun will come into a window. Or when a slope will block out the afternoon sunshine. You can calculate the height of a building or a tree by pacing out the distance from the tree to where you make your angular measurement.

Consulting a set of trigonometric tables, the tan ratio (opposite over adjacent) for the relevant angle will give you the ratio of the height to the lateral distance. If your feet gave you 30m, and your fists gave you 30 degrees, the tan table for 30 degrees gives you .5776; so h/30 = .5776, so h = 17.32m. Occasionally you might want to know the distance from the low corner to the top corner; for this you need the lateral distance, the angle, and the cosine (adjacent over hypotenuse) ratio for that angle. Sometimes you know the height and want to know how far the shadow will be cast; the tangent ratio will give you this as well. With a bit of practice, and some simple maths, you can now do some quite sophisticated surveying, at virtually no cost.