I will treat the aircraft as a particle, instant and constant speed will be assumed, take of and landing times will be ignored. The aircrafts speed will be affected by the speed and direction on the wind. As we assume the aircraft speed, wind speed and direction will be constant; we can use vector diagrams to work out how long the journey will take. I will have my first base camp in the middle. I will then place the base camp at different areas in the circle, and see how this effects the journey time.
I will then work out a general formula for any speed of aircraft, wind speed and direction, so the journey time could be worked for any variables of these 3. Circle 1 – radius = 50km. First observation site – north (0? ). Resultant velocity will have to act from the base camp to the observation site. The time taken to reach the observation site west (270? ) of the base camp will be the same as the time taken to reach the observation site east of the base camp.
This is because the vector diagram travelling from the base camp to the east observation site will be the same the vector diagram from the west observation site to the base camp, and the vector diagram from the base camp site to the east observation site will be the same as the vector diagram travelling from the west observation site to the base camp. So total time taken to reach went observation site and return to base camp = 32 minutes. The results taken would not be very realistic, as the journey times are quite short take off and landing times will be significant.
In a place like the arctic take off and landing times would be very significant, as it would take variable and mostly long periods of time to get the aircraft prepared. The times would be variable because the weather is so unpredictable in the Arctic. The journey may only be, say 32 minutes, but the preparation time could be much longer. For a model of this simplicity, we don’t take into account this extra time for take offs and landings; we just treat the aircraft as a particle, assuming instantaneous and constant speed.
The speed of the wind is also unlikely to be constant in direction and speed. It is clear from the readings taken that a graph can be drawn that repeats itself after 180?. The time taken for 0? is the same as the time taken for 180? , and the total time for the site 90? is the same as the degree 180? later, 270?. I now need to derive a formula to calculate the time taken for any wind speed, aircraft speed and wind direction.