By Sean Mitchell
It happens to us all. We are in the field and we forgot our field tape on the desk in the office; accidentally backed the truck over our field vest holding the clinometer; we dropped the laser rangefinder in the deepest part of the river; our batteries pack it in and we don’t have spares… Not having functioning equipment does not necessarily mean not collecting data. It simply means we need to improvise. Some of the most common things we may need to do — whether we have our GPS, compass, and clinometer or not — are to determine direction, measure length and distance, calculate heights, and determine level. Below are a handful of alternative, ’old-school’, approaches for those times that you are stuck.
Direction without a compass
Lacking a compass you can still easily determine the cardinal directions, without looking for moss on trees, measuring shadows, or waiting for nightfall to show you the north star. What time is it? Now imagine an analog clock face with that time shown. Point the hour hand of the clock face at the sun. Halfway between that direction and 12:00 on the clock – by the shortest route – indicates due south. For example: You arrive on site at 10:00 AM. Point the hour hand at the sun. Now determine the mid-point between 10:00 and 12:00 (11:00 in this case; you want to go the shortest route to the 12:00). The direction of 11:00 AM is due south. From this you then know other cardinal points.
Length and distance without a tape
When you don’t have a tool for measuring distance, use your own paces. It is an old technique but still very valuable in a pinch. In comparing my pacing with measured distances I am regularly within 10% and with care, and dependent upon the terrain of course, can be within 5%. It is worthwhile to know your average pace length before going in the field, but even if you don’t you can still record number of paces then back-calculate after determining your pace length later when you have access to a measuring instrument. Be aware, however, that pace length varies whether the ground is flat or inclined, whether you are travelling upslope or downslope. Obviously this will not give you engineering-level accuracy, but when you want to estimate length to a feature or object, this is better than our usual visual estimate.
Pacing works well when you can walk the distance between points, but what about when you cannot? Such as estimating width of a wide river or a canyon. Here, we appeal to basic trigonometry (Figure 1). If we can know the length of a baseline along one side of the river or canyon (such as by pacing it out to 50 paces), and the angle (α) to a feature on the opposite side (from a compass bearing, cross-staff [see below], or even a visual estimate), trigonometry then tells us that:
Opposite = tan ( α ) * baseline
So, with a 50 pace baseline, and α of 28°, our river width is:
Tan 28° * 50 paces = 26.5 paces.
Figure 1: Schematic of determining river width from only a baseline distance and angle.
Height without a clinometer
This same trigonometry can be applied to height when we lack our clinometer; we simply turn the geometry to the vertical. Lacking modern tools we can revert to a five hundred year old technology — the cross-staff (Figure 2). Here we are going to determine the opposite and adjacent legs of a right-angle triangle we make. Taking a large stick (a staff) we extend it horizontally, as near level as we can. Then sliding a smaller stick along the horizontal staff we find the point at which, when viewing our object at height (let’s say a falcon nest on a cliff face), our line of sight extends from the rear of the staff to the top of the stick (I reiterate, the staff must be level for this to work). We then measure the distance along the staff (adjacent in out triangle), and the height of the stick from the staff (opposite in our triangle), and from this calculate our viewing angle. Knowing our angle, we then pace our distance to the cliff and determine the height to falcon nest using the same equation as above.
This cross staff is typically used vertically, but it works equally well horizontally to determine an angle; it could be used to measure angle α to estimate the river distance above. Or, if you previously determined the cardinal points from the sun, you could even estimate compass bearings from this technique.
The key take-home when using trigonometry for height or distance is you need two things: the angle α and a distance of the adjacent leg. With only these two things we can accurately estimate heights and distances. How α and adjacent length are measured… well, that is where the improvisation can come in.
Establishing level without a level
Sometimes we want to establish level with some degree of confidence. But, oh bother, we dropped our level into the canyon we were measuring above. An old and simple method to establish level without instruments is to nearly-fill a shallow pan of some sort. This could be litter you have picked up, a cut down pop bottle, any shallow container that will hold water. The water surface, which will always remain horizontal, is then used as your reference and the surface prepared – shimmed up or cut down – until the pan of water is level.
These are only a few useful tips and tricks picked up over years of field work (and more frequently than I like not having the tools to do the job properly). They are not necessarily highly accurate – though you would be surprised how on-the-nose they are when care is taken – but will at least allow you to collect data. Familiarity with basic trigonometry and an open mind to improvisation can ensure you do not have a wasted day when you, inevitably, end up forgetting, losing, or breaking an important measuring instrument.