by tonytran2015 (Melbourne, Australia).
When you are outdoor, you often need to work out the distances to various objects around you so that you can plan your activities and know exactly where you are on your map to be in control of your trip, to make your plan to get back to safety, or to inform your rescuers of your exact position. However the challenge arises you have to make angle and distance measurements but neither can nor should employ any instrument, such as when hiking, when riding a motor-bike, or when on a touring bus. In such cases measuring angles with bare hands is the only method left. (Accurate measurement of angles allows determination of distances in survival situations.)
The method is described here and it uses the edges of the index and middle fingers as parallel guide lines for measuring angles. (Measuring posture must be correct to keep the viewing angles separating them nearly constant.)
Step 1: Frontal Measurement of Angular Separation at Eyes Level (Basic Posture).
Figure: Basic arm posture for angle measurement. The two outer edges of the measuring fingers form the marks on a scale of 0 to 10 for measuring vertical angular separations. The fraction of (10/200)rad in this figure is only for an angle of 3 degrees, the denominator will be different for other values of the angle.
This measurement uses the basic posture for angle measurements.
User has his face and chest facing the object to be measured. His shoulders are kept level, one of his arms stretched out, to have its measuring fingers precisely in front and on the symmetry plane of the torso.
The index and middle fingers of that hand are curled. The two outermost joints of each of these fingers are kept horizontal, straight and at right angle to his line of view. The edges of those finger extremities form three regularly spaced parallel guide lines to make a scale for measuring angles. The two outer edges are separated by an unchanged angle depending only on the bone structure of the user. This angle is constant over a long time for each individual and can be used to measure any angular separation. It can be easily measured by comparing it with the diameter of the Moon. It is usually between 2 and 5 degrees (which is 4 to 10 diameters of the Moon; each diameter sustains half a degree). The user must know how to find out the value for his own body structure:
1 finger has nearly 1.5 degree width in frontal measurement (for most people),
2 adjacent fingers have nearly 3 degree width in frontal measurement (for most people).
User can also have those index and middle fingers pointing in any direction from 1 to 7 o'clock to measure any non-vertical angular separation.
When the object in view is not level with eye level, the user can raise or lower his stretched arm, tilt his head and bend his upper torso to keep the distance from the measuring hand to the eyes constant. By raising and lowering the arm, the aiming line can reach an elevation of 80 degrees and a depression of 90 degrees.
Measurement of overhead angles is more difficult and has reduced distance from eyes to hand. The resulting angle must consequently be increased by some percentage to compensate for that.
To have consistent results, all other measuring postures should be immediately alternated with the basic posture to check for the constancy of the distance from eyes to hand.
Step 2: Conversion of the Angle Into Fractions of Radian or Mil.
Figure: The two outer edges of the measuring fingers form the marks at 0, 5 and 10 on a scale of 0 to 10 for measuring angular separations; the scale is oriented horizontally in this illustration. The fraction of (10/200)rad in this illustration is only for an angle of 3 degrees, the denominator will be different for other values of the angle.
The angle between the outer edges of the two fingers is next converted into a gradient (or slope) value which is more useful.
3 degrees is nearly equal to a slope of 0.0523 (= tan (3 degree) = 3*0.01745) which is next written as 1/19.12 = 10/191.2 # 10/200 (You can use 10/191 but rounding the ratio to 10/200 make field calculations much faster.).
The separation angle of 3 degree has thus been converted into an angle of (10/200) radian (see the step on Units for angle measurement).
Similarly, the separation angle of 4 degree is converted into an angle of (10/150) radian.
Each user has to determine the value for his own individual angle which is determined by his body structure, convert it into a fraction of one radian with a nominator of 10 and remember his own denominator value. The denominator may be any rounded numbers between 100 and 400.
The two outer edges of the measuring fingers thus form a scale from 0 to 10 for measuring angles. Angles are measured against the nominator of the fraction for the angle between the outer edges of the two fingers.
Readers may skip to Units for measuring angles on first reading.
Step 3: Measurement Over the Shoulder.
This is used when it is not practical to assume the basic posture, such as when standing on a tight spot.
User has one of his shoulder facing the object to be measured, his two shoulders in line with the object , the arm nearer to the object fully stretched out, its index and middle fingers placed between his eyes and the object. This is for measuring angle over the shoulder. The parallel guide lines formed by the fingers are now separated by a smaller angle. The angular separation of the guide lines is now reduced by about 25%.
Step 4: Measurement at 45 Degrees to Your Shoulder Line.
This is used when it is not practical to assume the basic posture, such as when standing on a tight spot.
User has his measuring arm stretched out, pointing to the object. The user can raise or lower his stretched arm and tilt his head and upper torso to keep the distance from the measuring hand to the eyes constant. By raising and lowering the arm, the aiming line can be reach elevation of 60 degrees and depression of 90 degrees. The angular separation of the guide lines is now reduced by about 20%.
Step 5: Units for Angle Measurement.
The angle for a full circle is divided into 360 degrees, or 2X(3.14159) radians. As it is not convenient to use any compass scale in radians, the US military compasses use their scales in mils. A full circle is divided into 6400mils, so
6400mil = 360degree = 2*3.14rad,
1 rad = 1019mil # 1000mil (This is a convenient conversion formula).
Quick reference values for angle measurement:
An equilateral triangle has 3 equal angles of 60°.
1 degree angle is equal to (2*3.14159/360)rad # (1/60)rad # a slope of (1/60).
6 degree angle is equal to (2*3.14159/60)rad # (1/10)rad # a slope of (1/10).
10 degree angle is equal to (2*3.14159/36)rad # (1/6)rad # a slope of (1/6).
The diameter of the Moon varies between 0.5degree and 0.55degree. It can be taken to be 1/2 degree and is used to conveniently calibrate the angular spacing of your index and middle fingers.
Step 6: Application 1- Estimating Distance to an Object of Known Size on the Ground.
Figure: A distinctive building with known dimension can be used to estimate your distance to it.
Objects of known sizes such as your companion and his survival walking stick or of standardized sizes such as train track widths, street signs, car lengths or of very similar sizes such as fully grown plants and animals can be used to estimate your distances to their nearby objects. Your distance to it is given by the simple formula:
(inverse of angle in radian) * (size of object) = (distance to object).
A numerical example will be given in Application 6.
Step 7: Application 2- Estimating Distance to an Intersection Along a Road of Constant Width.
Figure: A straight road of constant width. The arrows on the right correspond to the distance to the intersection, 1/2 and 1/4 of it.
(Estimating distance to an intersection along a straight road of constant width.)
The width of the road must be constant in this application. You first find an observation point higher than the surface of the road to observe the width of the road with SAFETY and ease.
Measure the angular width of the road at the intersection. The point on the road where the angular width is double that is at half the distance. The point on the road where the angular width is double that new width is again at half of that new distance. Use the method repeatedly to obtain 1/2, 1/4, 1/8, 1/16 of the unknown distance, until the last one in the sequences can be accurately estimated by any other method such as comparison to your height. Note that suitable adjustment should be made for the height of your observation point.
Step 8: Application 3- Estimating Distance to a Point Along a Straight Line on the Ground.
Figure: A straight yellow line to an object of unknown distance, which is placed at the smallest arrow on the line. Your observation point is at the center of the bottom edge of the figure. The arrows on the right correspond to the distance to the object, 1/2 and 1/4 of it.
You should choose an observation point on one side and away from the line. Imagine a parallel hand rail at your eye level on top of that line. The hand rail runs from your eye to the intersection of that line and the horizon. Use the method of the preceding section to repeatedly divide the distance into half until the last one so obtained can be accurately estimated by any other method such as comparison to your height.
Step 9: Application 4- Measuring Distance to a Ground Object by Traversing Horizontally.
Figure 1: A pole of unknown distance from the observer who is at the short base of the triangle drawn by the dotted line. Top inset: The pole seems to move against the distant background when the observer moves at right angle to the line of view. Figure 2: On the scale 0-5-10 formed by the edges of your two measuring finger, the pole seems to move by a value of 17. Figure 3: A movement at an oblique angle can be made and the traverse is obtained from the projection of this angle onto the normal to the line of view.
Measuring distance to a ground object by traversing horizontally is also known as measurement by parallax angle.
Notice the position of the object on the distant (far) skyline (or low clouds). Traverse 10 parade paces (7.5m) in a direction at right angle to the line of view. Observe the relative horizontal displacement of the impression of the object on the distant sky line and measure this angular displacement. (If at night, observe the relative horizontal displacement of the object against the low elevation stars and measure this angular displacement.)
(inverse of angle in radian) * (traverse) = (distance to object).
When it is not practical to move at right angle to the line of view, a movement at an oblique angle can be made and the traverse is obtained from the projection of this angle onto the normal to the line of view.
(The result will be more accurate when the traverse and the angle are determined more accurately such as when using a tape measure and an accurate sighting compass.)
1. The distance to a transmission tower may be known if the you can walk around it in a circle and measure the length of the circle.
Distance = (Length of circle)/(2*3.14)
When the whole circle cannot be made, part of it (a circular arc) can be used instead and the distance is given by
Distance = (Length of arc)*(360degrees/(angle of arc in degrees))/(2*3.14)
Distance = (Length of arc)*(6.28318radians/(angle of arc in radians))/(2*3.14)
Distance = (Length of arc)*(1radian/(angle of arc in radians))
2. If the direction to the transmission tower changes by 5 degrees (=5*0.0174 radian) after you have traversed 7.5m, as in Figure 1, the distance will be
(1/(5*0.0174))*(7.5m) = 86m.
The value of 5 degrees was supposed to be obtained by an accurate angle measuring device and is equal to the angle of the arc. The value of 5 degrees is only an example, you have to use whatever value given by your angle measuring device.
3. Since the transmission tower appears to move against the distant skyline when you traverse 7.5m, as in Figure 1, the angle of this movement relative to the distant skyline can also be used to work out your distance to the tower without using any measurement device as in the following.
We first assume the ratio measuring the angle between the outer edges of your two measuring fingers to be 10/200 (This is the ratio for most people). On the scale of 0-5-10 formed by the edges of your two measuring fingers, the transmission tower seems to move by a value of 17 units (which is a rough value of 5degrees (=0.087radian) read on a scale of (1/200)radian per unit) against the distance skyline (Figure 2). With this reading of 17, the distance to the tower can be worked out to be
(1/(200/17))*(7.5m) = 88m,
So, the distance has been worked out in a simple way with an error of about 5%, using only your bare hands.
4. If you are on moving along a track at 30° angle to the line of view, you don't have to leave it only to make a traverse at right angle to the line of view. Just keep moving along the track for about 15m, the transmission tower will move against the sky line by some angle. The traverse distance is now
Other calculations remain the same.
Step 10: Application 5- Measuring Distance to a Ground Object by Traversing Vertically.
Figure: A tree of unknown distance to observer. Inset: The horizon seems to follow the observer and moves against the tree when he stands up and crouches down.
Measuring distance to a ground object by traversing vertically.
Notice the position of the object on the distant (far) skyline (or low clouds). Crouch down and stand up to move your eyes at right angle to the line of view. Crouching reduce your eye level by half your height. Observe the relative vertical displacement of the impression of the object on the distant sky line and measure this angular displacement.
(inverse of angle in radian) * (change in height) = (distance to object).
Step 11: Application 6- Locating Your Position on a Map Relative to a Tall Land Mark.
Figure 1: The tall, distinctive building of step 6 is used as a landmark for navigation around the city. Figure 2: The location of the landmark on a map with distance scales. Notes on the map: The map data are used under Open License from Open Street Map, the data are owned by Open Street Map Contributors.
Use the known size of the distinguishable parts of the landmark for estimating of its distance (as given in preceding section). The direction of the landmark from the observation point gives the direction of the observation point relative to the landmark.
The landmark building is observed to be in the direction of 0° to 10° (North) of the observation point.
Measurement of the top segment of the landmark building by using the scale 0-10 of the method in step 1 gives a value of 6. The angle thus is (6/10)*(10/200)rad = (6/200)rad.
The top segment (from the helipad to the top) of this building has a height of 71m (from data provided on the internet). Therefore its distance from the observation point is
(200/6)*71m = 2400m (10% accuracy).
The observation point is thus on the thick faint red arc drawn on the map and in the direction 180°-190° (South) of the landmark.
So the observation point should be somewhere close to the Southern end of a bridge on the map.
This method for positioning is found to be quite good for this example as the actual observation point is right on the South end of that bridge.
Step 12: Estimating Distance by the Speed of Sound.
At the moment of seeing the cause, such as a firework, an explosion, you should start counting "one thousand and one, one thousand and two, one thousand and three, . ." . Your "one" , "two", "three" will correspond to 1second, 2seconds, 3seconds after the flashing. The sound will come against the your counting to give the time for the sound to come to you. It gives your distance from the source of the sound.
1 second corresponds to 340m, 2 second, 680m, 3 second, 1020m, . . .10 second, 3400m.
Estimating distances to thunder storms.
When you are outdoor in the wilderness, it is vital to avoid lightning strikes. Lightning strikes occurs when there is discharge to the ground by electrically highly charged clouds. Highly charged clouds usually discharge among themselves creating lightning flash. At the moment of flashing you should start counting "one thousand and one, one thousand and two, one thousand and three, . . " to determine your distance to the lightning discharge.
When the lightning strikes is closer than 2000m (that is when any thunder arrives within 6 seconds of its flash) you should think about your safety and your plan to avoid lightning strikes.