How do pilots use trigonometry

He tries to give you the facts from the source materials but maybe he got it wrong, maybe he is out of date. Sure, he warns you when he is giving you his personal techniques, but you should always follow your primary guidance Aircraft manuals, government regulations, etc.

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As a result, Gulfstream is not responsible or liable for your use of any materials or information obtained from this site. Trigonometry for Pilots Engineering.

Eddie sez:. Figure: Portraits von Pythagoras, from Wikimedia Commons. Last revision: Sum of Angles. Figure: Sum of angles in a triangle, from Eddie's notes. Sum of Legs. Figure: Right triangle legs, from Eddie's notes. Trigonometric Functions. Known: One angle, two sides, Find: Third side In aviation the triangles are often right angles, which means you will always know at least one of the angles. A Few Examples. Figure: Course azimuth deviation, from Eddie's notes. She asks the schoolkid next door to work it out for her.

The kid measured the shadow length from the tree. You should get 1. The angle between the diagonal line and the ground is the descent angle. For this example, we will say that we need that angle to be 3-degrees. Now we must determine how fast we need to lose altitude to keep that 3-degree glidepath angle as we approach the runway at a given speed.

To do this we need to use the formula:. Several data conversions are necessary because groundspeed is measured in nautical miles per hour whereas we want to solve for our descent rate which is expressed in feet per minute.

To start our conversions, we first use the formula:. If our groundspeed is kts and we divide that by 60, we get a speed of approximately 1. Now we need to convert this to feet per minute. Now that our groundspeed is expressed in feet per minute, we are ready to calculate the rate of descent we need to stay on glidepath.

When we multiply 10, feet per minute x the tangent of our 3-degree glidepath, we get a descent rate of feet per minute. This may sound complicated, but usually if you do the equation, you will use a calculator. Also, since 3-degrees is a common glideslope angle, pilots have worked out another rule of thumb that gets you close if you do not have a calculator to plug your equations into.

Simply take your groundspeed in knots and multiply it by 5 to arrive at an approximate descent rate of feet per minute which is very close to the precisely calculated feet per minute you get when using the equation. Pilot math can seem intimidating, but the important thing to remember is that if you understand the purpose and theory behind the equations, following the math itself often gets easier. Also, in many cases you can simply use a calculator or apply a rule of thumb estimation to arrive at a quick ballpark answer to a math question that does not require specificity.

If being a pilot is your dream, do not let the math scare you away. Instead invest some time in learning more about how pilots use math.

Sign up for our newsletter and be in the know. Receive coupons and special promotions! Your email. New customer? Create your account Lost password? Ready to learn what it takes and conquer your fear of pilot math? Here is what you need to know: What types of math do pilots? The later are fairly straight-forward; the former are more complex. Crosswind component is a simple tangent calculation.

Wind correction angles are more complex involving vector addition taking into account magnetic course, true airspeed, forecast wind angle, and forecast wind speed.

Now, the original question was merely, do pilots need to use trigonometry. The answer to that question is, "Yes". The question has since been edited to specify the use of trigonometry "directly, with trigonometry knowledge". The answer to that question is, "No" , pilots do not need to have a working understanding of trigonometry, though they do need to be capable of computing the above described wind problems. A pilot need not understand the trigonometry used by the calculator, slide rule, or FMS that he or she uses to perform these calculations.

I know good pilots who have no real working knowledge of trigonometry and do quite well without it. For a pilot flying in the IFR environment, wind correction calculation is less frequently a needed calculation since most navigational means provide for wind correction in some way.

This is especially true of GPS or RNAV navigation, because the ground track can be compared to the aircraft's heading to show wind correction angle. I think the best example of routine use of trigonometry by pilots is to calculate winds aloft.

The data a pilot has on hand is his compass heading and his airspeed and his altitude and his true bearing based upon passing landmarks on the ground. From this data he can calculate the wind direction and velocity he is witnessing at his location and altitude. Normally he would use a flight computer called an E6B which is a circular slide rule of sorts.

The E6B is easier to handle in turbulence than a pocket calculator.