Aviation Mathmatics

Question 1

How can you determine distance from a station knowing Speed, Time and Bearing change?

Answer 1

(TAS x Minutes) / Bearing Change = Distance from the station

Question 2

When tilting the radar how can you use degrees and distance and convert that into altitude of a storm?

Answer 2

1 degree = 100’ at 1 mile (1000’ at 10 miles)

Feet x Distance = Height

Question 3

The hydroplaning formula V HP=
80 psi
200 psi

Answer 3

V HP = 9√Tire Pressure
Example:
At 80 psi, the square root is about 9 (9x9=81). 9x9=81 kt.
At 200 psi, the square root is about 14 (14x14=196). 9x14=126 kt.

Question 4

Reciprocal Headings:
313
071
181
047
035
199
355

Answer 4

When initial heading < 180 : (Heading + 200) - 20

When initial heading > 180 : (Heading - 200) + 20

*Remember that last digit remains the same.

Question 5

Temperature Conversions:
0° C =
15° C =
30° C =
40° C =
100° C =

Answer 5

0° C = 32° F
15° C = 59° F
30° C = 86° F
40° C = 104° F
100 °C = 212 °F

° F = ((° C x 2) - 10%) + 32
° C = ((° F - 32) + 10%) / 2

Question 6

What is the equation to convert ° C to ° F?

Answer 6

° F = ((° C x 2) - 10%) + 32

Question 7

What is the equation to convert ° F to ° C?

Answer 7

° C = ((° F - 32) + 10%) / 2

Question 8

Standard temperature lapse rate:

Answer 8

2 °C (3.5 °F) per 1,000’ change in altitude up to 38,000’

Question 9

Moist adiabatic lapse rate:

Estimate possible cloud bases with a relatively close temperature / dewpoint spread:

Answer 9

2.5 °C (4.5 °F)
Find the difference between the surface temperature and the dew point. This value is known as the “spread”. Divide the spread by 2.5 , then multiply by 1000.

Question 10

Solve for ISA:
11,000
FL230
FL390

Answer 10

Multiply by 2 then subtract FROM 15 °C.
11 x 2 = 22; 15 - 22 = -7 °C
23 x 2 = 46; 15 - 46 = -31 °C
FL390 N/A. Standard lapse rate is only applied up to FL380.

Question 11

For every 0.01 in. Hg you change your altimeter how many feet does that change?
From 29.82 to 29.92 is how many feet?

Answer 11

0. 01 in. Hg = 10’

29. 92 - 29.82 = 0.10 = 100’

Question 12

The ATIS altimeter setting (QNH) is 29.79 in. Hg and the local airport elevation is 460’ MSL. What is the pressure altitude?

Answer 12

29.92 - 29.79 = 0.13 (130’)

130’ + 460’ = 590’

Question 13

As you are descending from FL350 for a landing, you forget to reset your altimeter to 30.57 in. Hg for the local airport QNH. What will your altimeter read after landing?

Answer 13

650’ low

Question 14

Explain the 3-to-1 rule of descent planning:

Answer 14

3-to-1 rule means that you take the altitude (in 1,000s of feet) you need to lose and multiply it by 3 to determine where to start down. This means we plan to fly 3 NM for every 1,000’ of altitude lost. To use this method, an aircraft should maintain a constant mach / indicated airspeed to stay on profile.

Rate of Descent = 5 x Groundspeed

Question 15

Explain the constant descent rate method:

Answer 15

Used when you want to choose and maintain a constant vertical speed and ground speed during the descent.

1. Altitude to lose / Vertical Speed = Minutes required to descend
2. Calculate the distance traveled during the time needed to make the descent. 60 kts = 1 NM/MIN.
   GS / 60 = NM/MIN
3. NM/MIN x Minutes = NM

Question 16

Explain a pitch attitude solution for descent planning:

Answer 16

Starting pitch attitude at cruise is zero and no changes will be made to the aircraft to affect pich. This method requires two pieces of information to work: Altitude to lose and Distance to lose it in.

1. Abeam the 10° nose-down pitch indicator line on the attitude indicator label this the distance you need to descend by.
2. Take the altitude to lose and project how far below the horizon this number would be in relation to the distance (10° down) and this is your nose low attitude.

Example: 12,000’ to lose in 36 miles = 12 is 1/3 of 36 so 3.3° nose down
(Distance then altitude)

Question 17

How do you determine a headwind and crosswind using a scientific calculator?

Answer 17

HW: Wind velocity x Cos angle
XW: Wind velocity x Sin angle

SOHCAHTOA
SOH – Sin&raquo_space; Opposite / Hypotenuse
CAH – Cos&raquo_space; Adjacent / Hypotenuse
TOA – Tan&raquo_space; Opposite / Adjancent

Question 18

What is a rule of thumb when calculating headwind or tailwind component at:
030 or 150:
045 or 135:
060 or 120:

Answer 18

030 or 150: 90% Almost all
045 or 135: 70% Two-thirds
060 or 120: 50% Half

Question 19

Crosswind Drift Angle formula:
Knots:
Mach:

Answer 19

Knots:

1. Convert speed into NM / minute (TAS / 60 = x)
2. Crosswind / x

Mach:

1. Mach x 10
2. One degree of crab per that number

Question 20

IAS to TAS:

Answer 20

Add 2% per thousand feet above MSL to your IAS.

KTAS = KIAS + (2 per 1,000’)

Question 21

NM to SM:

SM to NM:

Answer 21

NM to SM: NM x 1.15

SM to NM: SM x 0.87

To multiply decimals first multiply the two numbers without the decimal. Add the decimal spaces up and apply that to the answer.

Question 22

You are on a northerly heading and the VOR bearing pointer is showing a bearing of 260. Eight minutes later the bearing is 280. Your TAS is 420 KTAS and the winds are out of the north at 60 KTS. How far away is the VOR?

Answer 22

The key is miles traveled divided by radials multiplied by 60.

1. You are traveling at 360 knots GS (420-60=360) or 6 NM / min
2. In 8 minutes you have traveled 48 NM (8 min x 6 NM = 48 NM)
3. You have traveled 48 NM and 20 radials or 48 NM / 20 radials = 2.4 NM / radial
4. Therefore by applying the 60-1 rule: 60 x 2.4 = 144 NM from the VOR

Question 23

How do you find # of radials per mile?

Answer 23

of radials per mile = 60 + DME

Question 24

How to calculate degree lead point on an arc:

Answer 24

Degrees = (60/DME) x (NM/MIN - 2 (Turn Radius))

Question 25

What distance to turn to intercept a DME arc:

Answer 25

DME:

NM/MIN - 2 = Turn Radius