Performance/Pilot Math - PDF Free Download

Performance/Pilot Math Charath Ranganathan, AGI http://pfactor.io/ facebook.com/pfactor.io (chuh-ruh-th)

License This work is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License. Some images were first presented in the US Federal Aviation Administration s Pilot s Handbook of Aeronautical Knowledge. 2016 2

About Me Commercial pilot and AGI. Working on CFI. AvGeek both real, and sim. SoCal resident, originally from India. Day job: head of product development for an ecommerce startup in the direct-toconsumer wine business. Star Wars & Harry Potter nerd. Need to lose some weight! 2016 3

Outline Factors influencing aircraft performance. Takeoff and landing distance. Time, fuel, and distance to climb. Time/Speed/Distance calculations using E6B flight computer. Fuel calculations using E6B flight computer. Cruise performance. 2016 4

Performance Basics 2016 5

2016 6

Why Should I Care? To validate that you can safely operate the aircraft given the environment for your flight. Runway lengths Weather (especially, temperature) Fuel capacity, and reserves To ensure that your flight meets all FAA requirements, especially with regard to required fuel reserves. 2016 7

Factors Influencing Aircraft Performance Air density Less dense air reduces performance. Altitude Higher altitude lower performance. Temperature Higher temperature air is less dense. Hence, reduces performance. Humidity Increased humidity reduces density. Hence, reduces performance. 2016 8

Air Pressure Air has mass à exerts force. Since it s a fluid, force is exerted equally in all directions à Pressure. Pressure is measured in Inches of Mercury ( Hg) Millibars (mb) Standard atmosphere : 15 o C or 59 o F 29.92 Hg / 1013.2 mb 2016 9

Rules of Thumb Standard Temperature Lapse Rate Standard Pressure Lapse Rate 2 o C (3.5 o F) per 1,000 feet (up to 36,000 feet) 1 Hg per 1,000 feet (up to 10,000 feet) Memorize these numbers! 2016 10

Pressure Altitude Height above a theoretical level called the Standard Datum Plane. At the SDP, weight of the atmosphere is 29.92 Hg (1013.2mb). SDP could be above, at, or below, sea level depending on atmospheric pressure changes. Calculate by: Setting altimeter to 29.92 Hg Or, applying correction factor to indicated altitude depending on altimeter setting. 2016 11

Density Altitude Pressure altitude corrected for nonstandard temperature. Density of air varies with temperature, humidity, pressure. Temperatures higher than standard temperature lower air density. Lower air density affects aircraft performance: Power: reduced because engine takes in less air. Thrust: because propeller is less efficient. Lift: because thin air exerts less force on airfoils. 2016 12

Calculating Pressure Altitude Set the Kollsman window in your altimeter to 29.92. Altitude displayed by altimeter is the pressure altitude. Apply a correction factor to your current altimeter reading. Pressure Altitude = Indicated Altitude + Standard Pressure Altimeter Setting 1000 Say that you re at 5000 ft with altimeter setting of 30.02. Pressure Alt. = 5000 + 29.92 30.02 1000 Pressure Alt. =5000 + ( 0.1) 1000 Pressure Alt. = 5000 100 = 4,900 ft. 2016 13

Determining Density Altitude From previous slide Pressure Alt. = 4,900 ft. Say outside air temperature is 20 o C. Calculate density altitude: Draw a line on the chart parallel to the 5,000 ft line at what would be the 4,900 ft point. Draw a vertical line upward from 20 o C to meet the 4,900 ft line you just drew. At the point where the vertical line intersects the 4,900 ft line, draw a horizontal line. Read off the density altitude from the y-axis. Density Altitude = 6,600 ft. 1 2 3 2016 14

Takeoff and Landing Distances 2016 15

Best Angle vs. Best Rate of Climb Best angle of climb gives maximum altitude gain over distance. Fly at V x Use for obstruction avoidance. Best rate of climb gives maximum altitude gain over time. Fly at V y Use for normal climb. 2016 16

Takeoff Distances 2016 17

Takeoff Distance Sample Problem #1 Calculate the ground roll and distance over 50 ft obstacle given the following conditions: Short field technique Aircraft weight: 2,400 lbs. Airport pressure altitude: 2,000 ft. Outside air temperature: 20 o C Dry grass runway 9 kts headwind 2016 18

Takeoff Distance Chart 1. Read across the 2000 ft PA line to the 20oC columns. Ground roll = 1115 ft. To clear 50 ft obs = 2060 ft. 2. Dry grass runway: Increase ground roll by 15%. 15% of 1115 = 167.25. Ground roll = 1115 + 167.25 = 1282.25 ft 3. Headwind: Decrease distances by 10%. 10% of 1282.25 = 128.22 Ground roll = 1282.25 128.22 = 1154.03 ft. To clear 50 ft obs = 2060 - (2060x10%) = 2060-206 = 1854 ft. 2016 19

Takeoff Distance Sample Problem #2 Calculate the ground roll and distance over 50 ft obstacle given the following conditions: Short field technique Aircraft weight: 2,400 lbs. Airport pressure altitude: 2,000 ft. Outside air temperature: 17 o C 2016 20

Steps 1. Go to the 2000 ft. pressure altitude row. 2. Note down the values for ground roll & total distance at 10oC (1,035 & 1,910 ft.) 3. Note down the values for ground roll & total distance at 20oC (1,115 & 2,060 ft.) 4. Interpolate (refer next slide) 2016 21

Interpolation Ground Roll: Total to Clear 50 foot Obstacle: Ground roll at 20 o C 1,115 Distance at 20 o C 2,060 Ground roll at 10 o C 1,035 Distance at 10 o C 1,910 Difference 80 Difference 150 Increase in ground roll per o C = 80/(20-10) = 8 Increase in distance per o C = 150/(20-10) = 15 Increase in ground roll for 7 o C (17-10 = 7) = 7 x 8 = 56 Ground roll at 17 o C = 1,035 + 56 = 1,091 ft. Increase in distance for 7 o C (17-10 = 7) = 15 x 8 = 120 Total to clear 50 foot obstacle at 17 o C = 1,910 + 120 = 2,030 ft. 2016 22

Landing Distances 2016 23

Landing Distance Sample Problem Find the ground roll and total distance to clear a 50 ft. obstacle given the following: Airport pressure altitude: 4,000 ft. Temperature: 15 o C Aircraft weight: 2,400 lbs. Wind: 6 kts. headwind 2016 24

2016 Reference Line Reference Line Reference Line Landing Distance Chart 25

Reference Line Reference Line Draw a vertical line from 15oC to intersect the 4,000 ft Pr. Alt. line. Reference Line Landing Distance Chart 1 2016 26

Reference Line Draw a horizontal line from the 4,000 ft Pr. Alt. line until it meets the Weight Reference Line Reference Line Reference Line Landing Distance Chart 2 2016 27

Reference Line From the weight ref. line, draw a line parallel to the black line until it intersects the 2,400 lb. mark. (Interpolation in action!) Reference Line Reference Line Landing Distance Chart 3 2016 28

Draw a horizontal line until it hits the Wind reference line. Reference Line Reference Line Reference Line Landing Distance Chart 4 2016 29

Reference Line Reference Line Reference Line Landing Distance Chart Draw a line that s parallel to the black wind lines until it meets the 6kt. Headwind mark. 5 2016 30

Reference Line Reference Line Reference Line Landing Distance Chart Draw a horizontal line until it hits the Obstacle height reference line. 6 2016 31

Reference Line Reference Line Reference Line Landing Distance Chart Extend the line horizontally to read the ground roll (~900 ft) 7 2016 32

Follow the black line upward to read the total distance over a 50 ft obstacle (~1,450 ft.) Reference Line Reference Line Reference Line Landing Distance Chart 8 2016 33

Reference Line Reference Line Reference Line Landing Distance Chart 8 3 4 5 6 7 2 1 2016 34

Time, Fuel, and Distance to Climb Used to determine: How long it will take to reach cruising altitude. How much fuel will be consumed in the climb. How much distance (on the ground) will the aircraft travel while climbing. Sample Problem: Calculate the time, fuel & distance for the following situation: Airport Pr. Alt.: 6,000 ft. Airport temperature: 25 o C Cruise Pr. Alt.: 10,000 ft. Cruise temperature: 10 o C 2016 35

Time, Fuel & Distance to Climb Chart 2016 36

Time, Fuel & Distance to Climb Chart Determine the values for the cruise P.Alt. and cruise OAT: Fuel = 6 gal Time = 10.5 min Distance = 15 nm 1 2016 37

Time, Fuel & Distance to Climb Chart Determine the values for the airport P.Alt. and OAT: Fuel = 3.5 gal Time = 6 min Distance = 9 nm 2 2016 38

Time, Fuel & Distance to Climb Chart Subtract 2 from 1: Fuel = 6.0-3.5 = 2.5 gal Time = 10.5-6.0 = 4.5 min Distance = 15.0-9.0 = 6.0 nm 1 2 2016 39

Cruise Performance Cruise performance charts (or tables) help to answer the following questions for a given cruise situation (altitude, engine RPM): True Airspeed (TAS) Fuel burn (gph) Endurance (hours) Range (miles) Sample Problem: Calculate the TAS, fuel burn rate, endurance and range for the following cruise conditions: Cruise Pr. Alt.: 5,000 ft. Engine RPM: 2,400 Assume standard conditions. 2016 40

Cruise Performance Table 1. Look for the 5,000 ft. altitude section. 2. Find the row corresponding to engine RPM (2,400 rpm). 3. Read across: TAS = 116 mph Fuel burn = 6.9 gph Endurance = 5.5 hrs Range = 635 miles For other situations, interpolate. 2016 41

Crosswind Component Headwind = 27 kts. Crosswind = 15 kts. 2016 42

Time/Speed/Distance Computations 2016 43

E6B Flight Computer Circular slide rule. Front has: Inner (movable) scale. Outer (fixed) scale. Front is used for basic calculations: Density altitude. Airspeed correction (CAS / TAS). Speed / Distance / Time. Fuel burn rate / time / fuel burn. Also can convert among units (sm to nm, mph to knots, etc.) Play with it: http://www.privatepilotstudy.com/e6b/front http://www.privatepilotstudy.com/e6b/back 2016 44

Density Altitude Calculation Using the E6B, find the density altitude for the following conditions: Pressure Altitude: 5,000 ft. OAT: 20 o C 2016 45

Density Altitude Calculation (contd.) 1. Locate the pressure altitude in the inner window (5,000 ft) 1 2016 46

Density Altitude Calculation (contd.) 1. Locate the pressure altitude in the inner window (5,000 ft) 2. Rotate the scale so that the OAT on the outer scale lines up with the pressure altitude (20 o C) 3. Read the density altitude against the arrow on the Density Altitude window (6,600 ft). 1 3 2 2016 48

Time/Speed/Distance Given two of the variables, find the third. For example How long would it take for you to cover 120 nm at a speed of 90 knots? (Estimated Time Enroute ETE) If you are flying at 120 knots, how far will you travel in 45 minutes? If you cross your first waypoint at 10:20AM and your second waypoint at 10:30AM, and your waypoints are 20 nm apart, what is your ground speed? Formula Speed = Distance Time 2016 49

Calculate Time 1. Set Rate Pointer at the speed on outer dial (90 knots) Rate pointer is always set to the per value (e.g. Knots = nm per hour) 1 2016 50

Calculate Time 2 1. Set Rate Pointer at the speed on outer dial (90 knots) Rate pointer is always set to the per value (e.g. Knots = nm per hour) 2. Locate the distance on the outer scale (120 nm) Outer scale always shows the numerator of the fraction (in this case, distance). 3. Read the time taken to fly 120 nm at 90 knots on the inner scale (80 minutes / 1:20) Inner scale always shows the denominator of the fraction (in this case, time). 1 3 2016 52

Calculate Distance? 120 = 45 min 1. Set the Rate pointer at the per value (120 nm per hour) 1 2016 53

Calculate Distance? 120 = 45 min 1. Set the Rate pointer at the per value (120 nm per hour) 2. Locate the denominator (45 min) on the inner scale. 2 1 2016 54

3 Calculate Distance? 120 = 45 min 1. Set the Rate pointer at the per value (120 nm per hour) 2. Locate the denominator (45 min) on the inner scale. 3. Read the numerator (distance travelled) on the outer scale (90 nm) 2 1 2016 55

Calculate Speed 20 nm? = 10 min 1. Locate 10 min (denominator) on the inner scale. 1 2016 56

Calculate Speed 20 nm? = 10 min 1. Locate 10 min (denominator) on the inner scale. 2. Rotate the inner scale to line up with the numerator (20 nm) on the outer scale. 1 2 2016 57

Calculate Speed 20 nm? = 10 min 1. Locate 10 min (denominator) on the inner scale. 2. Rotate the inner scale to line up with the numerator (20 nm) on the outer scale. 3. Read the speed against the Rate pointer (120 knots) 3 1 2 2016 58

Fuel Calculations 2016 59

Fuel Calculations Given two of the variables, find the third. For example If you are burning 12 gallons of fuel per hour, and it takes you 20 minutes to travel between two points on your flight, how much fuel did you burn? If you are burning 12 gallons of fuel per hour, and you are carrying 75 gallons of fuel, how much flight time do you have left? Formula Fuel burn rate (gph) = Fuel Quantity (gal) Time 2016 60

Calculate Fuel Used? gal 12 gph = 20 min 1. Set the rate pointer to the per value (12 gal per hour) 1 2016 61

Calculate Fuel Used? gal 12 gph = 20 min 1. Set the rate pointer to the per value (12 gal per hour) 2. Locate the denominator (20 min) on the inner scale. 2 1 2016 62

Calculate Fuel Used? gal 12 gph = 20 min 1. Set the rate pointer to the per value (12 gal per hour) 2. Locate the denominator (20 min) on the inner scale. 3. Read the numerator (fuel used) on the outer scale (4.0 gal). 3 2 1 2016 63

Calculate Flight Time Remaining 75 gal 12 gph =? min 1. Set the rate pointer to the per value (12 gal per hour) 1 2016 64

Calculate Flight Time Remaining 75 gal 12 gph =? min 1. Set the rate pointer to the per value (12 gal per hour). 2. Locate the numerator (75 gal) on the outer scale. 2 1 2016 65

Calculate Flight Time Remaining 75 gal 12 gph =? min 1. Set the rate pointer to the per value (12 gal per hour). 2. Locate the numerator (75 gal) on the outer scale. 3. Read the denominator (flight time remaining) on the inner scale (375 min. or 6 hr. 15 min) 2 3 1 2016 66

Wrap-up Aircraft performance is affected by changes in air density. Pressure altitude corrected for nonstandard temperature is called density altitude, and is the basis for many performance calculations. Interpolation is a technique used to calculate values in between two specified values, assuming a linear relationship exists in that range. The E6B contains an inner rotating scale, and an outer fixed scale. The rate pointer of the E6B is always set to the per value (miles per hour, gallons per hour, etc.) The outer scale of the E6B shows the numerator, and the inner scale shows the denominator, when performing rate calculations. 2016 67

Next Steps Review the Pilot s Handbook of Aeronautical Knowledge (Chapter 11) http://goo.gl/jjldv1 Visit my web site (under construction): http://pfactor.io/ Subscribe to my mailing list (subscribe box is on top right) Like, and subscribe to, my Facebook page https://facebook.com/pfactor.io/ If you need further training, let s talk Email address is on last slide. 2016 68

Thank You! charath@pfactor.io http://pfactor.io/ facebook.com/pfactor.io