01-F: Performance and limitations

Knowledge

Operating Limitions
- O in ARROW documents
- generally:
  - POH + placards
- comprehennsively:
  - the FAA-approved flight manual / POH
  - approved manual material
  - markings,
  - placards, and combination thereof
Weight and Balance Limitations
- W in ARROW documents
- generally
  - POH + equipment weight and aircraft weighing sheet
main elements of aircraft performance
- takeoff and landing distance
- rate of climb
- service ceiling (altitude above which climb rates drops below 100 FPM)
- absolute ceiling (altitude at which climb rate drops to 0 FPM)
- payload
- range
- speed
- fuel economy
- maneuverability
- stability
[Plank and Weight] Weight and Balance Diagram (Figure 60):
- current situation
  - principles
    - weight x arm = momentum
    - divide by 2 to obtain center of mass of the plank
  - left:
    - plank: 200 lbs x (45" - 15") / 2 = 200 x 15 = 3000 lbs-in
    - weight: 500 lbs x 15" = 5000 + 2500 = 7500 lbs-in
    - total = 10500 lbs-in
  - right:
    - plank: 200 lbs x (45" + 15") / 2 = 200 x 30 lbs-in = 6000 lbs-in
    - weigt: 250 lbs x 20" = 5000 lbs-in
    - total = 11000 lbs-in
- assessment
  - the left side has less momentum
  - to add momentum, we need to move the weight to the left
  - there is only one alternative in the question that moves the weight to the left, and that is by 1 inch
  - we see that this will add 500 lbs which is exactly what's missing
  - for an analytical solution, formulate arm of weight as variable X (no need, no one expects 7th grade math, they stop at 4th grade)
[Plank and Weight 2] Weight and Balance Diagram (Figure 61):

component	weight	arm	moment
weight X	50 lbs	50 in	2500 lbs-in
weight Y	?	25 in	?
weight Z	100 lbs	100 in	10000 lbs-in

right side: 10000
left side lacks 7500 lbs-in of moment. 7500 lbs-in / 25 in = 300 lbs
task wronly assumes that the plank does not weigh anything
Airplane Landing Distance Graph (Figure 37) and Airplane Takeoff Distance Graph (Figure 40)
- usage
  - phase 1
    - don't intersect with the given black lines
    - 1) instead mentally interpolate the actual curve we would be intersecting if it were drawn
    - 2) find the point where the point projected from the x-axis meets the imaginary line
    - 3) then project that point two the right to the next graph
  - phase 2
    - again, don't follow the given black curves
    - 1) instead use the point projected to the vertical reference line to imagine the next black line
    - 2) find our point of interest on that imagined black line given the value on the x-axis
Airplane Weight and Balance Diagram (Figure 32)
- passenger relocation task
  - current situation:
    - total airplane weight (given in the task): 2690 lbs
    - total moment (given in the task): 226'000 lbs-in
    - current CG arm (computed): 226000/2690 = 84 in
  - updates (front passenger leaves, and rear passengers moves to the front):
    - reduction 1 by
      - weight (given in the task): 180 lbs
      - arm (look-up in the table): 85 in
      - moment: 180 lbs * 85 in = 15300
    - reduction 2 by
      - weight (given in the task): 204 lbs
      - arm (look-up in the table): 121 in
      - moment: 204 * 121 in = 24684 lbs-in
    - addition of
      - weight (given in the task): 204 lbs
      - arm (look-up in the table): 85 in
      - moment: 20 lbs * 85 in = 17340` lbs-in
    - total update
      - -22644 lbs-in
      - -180 lbs
- new situation
  - total weight: 2690-180 = 2510 lbs
  - new total moment = 203356 lbs-in
  - new derived CG arm = 203356 lbs-in / 2510 lbs = 81 in
- answer
  - the CG arm changes from 84 in to 81 in, moving forward 3 inches
- fuel transfer/drain task

component	weight (lbs)	arm	moment
empty	2015	-	155400
front pax	425	85	36125
rear pax	300	121	36300
fuel (44 gal)	264	75	19800
total	3004	82	247625
max weight: 2950
- we have to loose 54 lbs ~ 9 gallons

balancing task:

given from text: - front pax: 411 lbs - rear pax: 100 lbs - wing tanks: 44 gal

looking up infromation from Figure 32, we obtain:

component	weight (lbs)	arm	moment
empty	2015	-	155400
front pax	411	85	34935
rear pax	100	121	12100
fuel (44 gal)	264	75	19800
total	2790	79.6	222235

at weight 2790, we are at a total moment of 2222, but Figure 32 requires at least a moment of 2243 at that weight
thus, we need to increase the number
moment is weight x arm, so we need to increase weight or increase arm away from the standard datum plane (i.e., move to the back)
options
- transfer fuel into the aux tanks
  - weight statys
  - updated total moment:
    - total moment:
      - reduce by 10 gal * 6 lbs / gal * 75 in = 4500
      - increase by 10 gal * 6 lbs/gal * 94 = 5640
    - 2222.35 - 45 + 56.4 = 2233.75
    - new arm: 80.1
  - result
    - arm is still too little (2233.75 < 2243)
- fill the auxillary fuel tanks
  - add 10 gal * 6 lbs/gal * 94 = 5640 to weight and total moment
  - new weight = 2850
  - new moment = 227875
  - new arm = 79.96
  - at a weight of 2850, Figure 33 requires a moment of at least 2309
- add a 100 pound weight to the baggage compartment
  - considerations
    - add 100 lbs * 140 in = 14000
    - new total moment = 236235
    - new total weight = 2890
    - new total arm = 81.47
  - result
    - new weight below max weight and above min weight
    - CG between 77.5 and 85.7
    - total moment of 2362.35 ~ 2362 within weight-specific range of 2354 and 2452
solution: add 100 pound weight
Crosswind Component Graph (Figure 36)
- wind decomposition taks
  - given
    - Runway 18
    - Winds as per tower: 220 at 30
  - derivations
    - Runway 18, i.e., facing 180°
    - angular difference between 180° and 220°: 40°
    - wind decomposition at 40° degrees on the 30° circle
      - H Wind: 23 kts
      - X Wind: 20 kts
  - cross-check with CX-3 Wind Component function
    - WSpd 30, WDir 220, Runway 18
      - X Wnd 19.28
      - H Wnd 22.98
- max wind task, i.e., asking for the maximum wind velocity
  - given
    - 30° winds
    - max demonstrated cross wind of 12 ktts
  - lookup
    - 1) find crosswind component on y
    - 2) find intersection with degree-specific radiating line
    - 3) imagine the circle on which the point lies
      - 22 kts
Load Factor Chart (Figure 2)
Velocity vs G-Loads / VG diagram (Figure 72)
- affects of gust on load factor
- enables to understand the effect of load factor on the airplane, e.g.
  - given 70 knots (converted with CX3 = 80.55 mph) and a load factor of 2, we end up in the upper left stall area, thus the airplane will stall
- lines
  - C to E: positive limit load factor
Airplane Weight and Balance Graph (Figure 34)

Given Component | Weight (lbs) | MOM/1000 ----------------------------|---------------|--------- empty weight | 1350 | 51.5 pilot and front passenger | 250 | - rear passenger | 400 | - baggage | - | - fuel, 30 gal | - | - oil, 8 qt | - | -0.2

filled 1) compute fuel weight 1 gal = 6 lbs 30 gal = 180 lbs

1) lookup oil weight from figure 1 qt = 1,875 lbs 8 qt = 15 lbs

1) compute arms from slopes in figure

Component	Weight (lbs)	MOM/1000	arm (from slopes in graph)
empty weight	1350	51.5	38.15
pilot and front passenger	250	9.4	37.6
rear passenger	400	28.5	71.25
baggage	-	-	90
fuel, 30 gal	180	7.5	41.6
oil, 8 qt	15	-0.2	-13
totals	2195	97.1	44.23

Component	Weight (lbs)	MOM/1000	arm (from slopes in graph)
empty weight	1350	51.5	38.15
pilot and front passenger	380	14.3	37.6
fuel, 30 gal	288	13.8	47.91
oil, 8 qt	15	-0.2	-13
totals	2033	79.4	38.66

In the question, we are offered 120, 105, or 110. - The envelope is capped at 2300 lbs. - As per weight column, we have 105 lbs left. - The whole moment and arm computation was not needed.

Weight and Balance Chart
- given:
  - airplane weight: 3000 lbs
  - total moment: 200'000 lbs-in
  - reduction
    - weight: 25 gal ~ 150 lbs
    - arm: 75 in
    - moment = 11250 lbs-in
    - resulting total moment: 188750 lbs-in ~ 1886 * 100 lbs-in
Density Altitude Chart
- given
  - start state:
    - temp: 90 °F
    - pressure altitude: 1250 ft
  - end state:
    - temp: 55 °F
    - pressure altitude: 1750 ft
  - lookups
    - start state: 3500
    - end state: 1800
    - diff: 1700 decrease
CG computation

given

component	weight	arm	moment
empty	1495	101.4	151593
front pax	380	64.0	4320
fuel (30)		96

1) fuel in gal x 6 2) weight x arm = moment 3) sum weight 4) sum moment 5) total arm = total moment / total weight

component	weight	arm	moment
empty	1495	101.4	151593
front pax	380	64.0	24320
fuel (30)	180	96	17280
total	2055	94	193193

Airplane Landing Distance Table (Figure 38)
- ensure to read properly
  - ground roll vs 50ft obstacle clearance distance
  - use multipliers (0.8, 0.9) for percentages
  - be ready to interpolate
self-explanatory
- Airplane Power Setting Table (Figure 35)

K2: Factors affecting performance, including

K2a: Atmospheric conditions

altitude definitions
- true altitude: altitude in MSL
- absolute altitude: altitude in AGL ([A]bsolute = [A]GL)
- pressure altitude: true altitude corrected for non-standard pressure
  - Equivalent definitions:
    - True altitude corrected for non-standard pressure
    - The altitude indicated when the barometric pressure scale is set to 29.92.
  - coincides with true altitude
    - under standard atmospheric conditions (question offers answer: when the atmospheric perssure is 29.92 inHg but does not specify "at surface")
- density alitude: pressure altitude corrected for non-standard temperature
  - underlying air density equation
    - rho = absolute pressure / (absolute temperature x specific gas constant)
  - thus, density depends on
    - pressure
    - temperature
  - equivalent definitions of density altitude
    - pressure altitude corrected for nonstandard temperature
    - altitude at which a given density if found in ISA conditions
  - density altitude increases as the air gets less dense ("thinner")
    - the air gets thinner
      - as pressure decreases
      - as temperature increases
      - as humidity increases
- indicated alitude: altitude given the current Kollsman window altimeter setting
performance decreases
- as density altitude increases, i.e.,
  - as temperature increases increase
  - as relative humidity increases
  - as air pressure decreases
- reduced performance of
  - the wings
  - the propeller
  - the engine
altimeter error
- on warm days, indicated altitude reads lower than true altitude
  - the air and its pressure levels expands
  - the aircraft is at a true altitude, but experiences the pressure of a lower altitude
  - it reads low, we are above the indicated altitude
  - we are safe from terrain, but might bust airspace above
- on cold days, indicate altitude reads higher than true altitude (dangerous!)
  - vice versa

K2b: Pilot technique

Four flight fundamentals in aircraft maneuvering:
- straight-and-level
- turns
- climb
- descent
climb v-speeds
- Vx: best angle of climb / climb for the shortest distance
- Vy: best rate of climb / climb for the shortest period of time
attitude indicator is the foundation for all instrument flight
trim releves the pilot of the need to maintain constant pressure on the flight controls
loss of situational awareness during maneuvering
- LOCI: loss of control in-flight
  - risk management via UPRT (upset prevent and recovery training)
- CFIT: controlled flight into terrain

K2c: Airplane configuration

K2d: Airport environment

landing:
- gust factor: difference between peak wind speed and sustained wind speed
- add half the gust factor in gusty conditions to the approach speed

K2e: Loading

1 gal ~ 6.01 pds
load factor
- influenced by
  - bank angle (assuming level turn)
    - dependes on the bank angle, not the airplane speed or airplane type
    - n = L / W where L is lift (= air load) and W is aircraft weight
    - in a level turn, the total lift L is decomposed in vertical (L \cdot cos(theta)) and horizontal component (L \cdot sin> (theta) )
    - computation of load factor is independent on airspeed or specific aircraft
    - computation of n in a bank: n = 1 / cos(theta) (https://chatgpt.com/c/681e2879-0e30-8001-bfe5-a0baec8f393a)
      - 45 degs: 1.41
      - 60 degs: 2
    - substantially increases after 45 degrees
  - gusts and turbulence
  - speed
- does not increase in
  - steady climbs (in fact lift is reduced, and thrust pulls us more)
  - stalls (in fact close to no lift is generated during a stall)
- increases stall speed
  - V_s: stall speed
  - n: load factor
  - V_accelerated_stall = V_s x sqrt(n)
the amount of excess load that can be imposed on the wings
- depends on the speed of airplane
  - abruptness will cause
    - stalls below maneuvering speed
    - structural damage above maneuvering speed
loading the aircraft beyond its maximum take-off weigth
- increases stall speed
- increases take-off distance
- increases landing roll
- decreases rate of climb
Va: maneuvering speed
- definition:
  - the speed below which the airplane will rather stall than break when applying maximum control input once and on a single control input
  - above the maneuvering speed, the airplane might break from the g-loads from sudden forces of maximum elevator, rudder or aileron, esp. at repeated or simulanteaous inputs, instead of just stalling
- explanation:
  - The aircraft breaks at a fixed g load (lift divided by weight).
  - In straight and level l/w = 1g
  - In climbs, l/w > 1.
  - If we remove mass from the aircraft (imagine we drop out stuff out of the window), the l/w ratio of the aircraft immediately increases, because at the same angle of attack and at the same speed, we produce the same lift, which now exceeds weight.
- influence factors:
  - as becomes clear from th explanation
  - the maneuvering speed decreases as the airplane gets lighter because control surface effectiveness increases as the > airplane gets lighter
  - example:
    - 2450 lbs: 99 KIAS
    - 2000 lbs: 92 KIAS
    - 1600 lbs: 82 KIAS
- indication on the airspeed indicator:
  - none, only shown on a placard
- resources:
  - https://www.youtube.com/watch?v=N3M4k6ChQL4
  - https://www.youtube.com/watch?v=XN0LVBff_5g

K2f: Weight and balance

weight definitions
- standard empty weight
  - includes
    - airframe
    - power plant
    - unusable fuel and undrainable oil
    - full oil
  - does not include
    - full fuel tanks
- basic empty weight: same as the standard airplane plus optional equipment
- gross weight = maximum allgowable weight of the airplane with its contents
  - maximum ramp weight
  - maximum takeoff weight
  - maxumum landing weight
moment = weight x arm
modern aircraft are designed such that
- at
  - full occupation of seats
  - full fuels
  - full baggage compartment
- the aircraft is grossly overloaded
overloading causes
- higher takeoff speed
- longer takeoff run
- reduced rate and angle of climb
- lower maximum altitude
- shorter range
- reduced cruising speed
- reduced maneuverability
- higher stalling speed
- higher landing speed
- longer landing roll
- excessive weight on the nose wheel
CG
- in-lmimits effects
  - forward CG
    - principle
      - tailplane (horizontal stabilizer + elevator)
        
        acts like an inverted wing
      - increased elevator-up deflection is needed to keep the nose up, thus increasing the downward force on the tailplane and the airplane overall
    - effect on
      - cruise speed
        
        more lift needs to be generated by increasing angle of attack, thus increasing drag at the same speed
        
        part of the cruise power setting (say 75%) is used to counteract the increase in drag
      - stall speed
        
        increased load leads to accelerated stall speed
      - stability
        
        increased moment ledas to increased longitudinal stability
  - rearward CG
    - principle
      - decreased elevator-up deflection is needed to keep nose up, thus decreasing overall downward force
    - effect on
      - cruise speed
        
        smaller angle of attack, thus less drag, thus lower stall speed
      - stall speed
        
        less wing loading, thus lower stall
      - stability
        
        shorter arm, thus less stable, and more difficult stall and spin recovery
- out-of-limits
  - forward of the CG limit increases nose heaviness, thus
    - requiring more backpressure to hold the nose up
    - potentially exceeding elevator authority and rendering it impossible to flare for landing
  - aft of the allowable range
    - decreases pitch stability, thus also
      - producing very light control forces that easily allow overstressing the aircraft
    - increases tail heaviness, thus
      - rendering it potentially impossible to recover from stalls and spins
stability
- aircraft coordinate system
  - roll axis = longitudinal axis (aileron controlled)
  - pitch axis = laterial axis (elevator controlled)
  - yaw axis = vertical axis (rudder controlled)
- refence coordinate frames
  - body frame (centered in the CG and aligned with airplane body's axes)
  - wind / stability frame (centered in the CG and aligned with the relative wind axis / aircraft velocity vector)
- stability planes
  - stability axis deviate from the correspondence with the respective axis
    - e.g., longitudinal stability refers to pitch stability (not roll stability despite the longitudinal axis representing the roll axis)
  - planes (as in planar surfaces) of stabilty
    - longitudinal stability = pitch stability
    - directional stability = yaw stability
    - lateral stability = roll stability
- Static stabilty vs dynamic stability
  - core questions (example: pitch stability = longitudinal stability)
    - static stability: In trimmed flight (= straight-and-level, unacclerated flight), if I pitch up, does the center of gravity create a pitch-down moment (i.e., is there enough) to revert back to neutral?
    - dynamical stability: If yes (i.e., statically stable), is the moment (i.e., arm and weight) not too much such that I enter many aggravating oscillations or not?
  - time horizon
    - static stability: considers up to a single oscillation (potentially none if aircraft is unstable and does not swing back)
    - dynamic stability: considers trend in multiple consecutive oscillations
  - types
    - static stabiltiy
      - statically stable: deviation from trimmed flight is counteracted
      - statically neutral: deviation from trimmed flight is exactly maintained
      - statically unstable: deviation from trimmed flight is aggravated
    - dynamic stabilty:
      - only considered in case of a statically stable aircraft (otherwise there will be no oscillations and the aircraft will keep or aggravate its previous direction of disturbance)
      - dynamically stable: amplitude of oscillations damp out restoring trimmed flight
      - dynamically neutral: amplitude of oscillations stays constant without aggravating but also without returning to trimmed flight
      - statically unstable: amplitude of oscillations increases aggravating the pitch motion with each oscillation
  - major influence on stability per axes
    - longitudinal (i.e., pitch) stability
      - relationship between CG location and center of pressure (CG must be ahead of CP)
    - lateral (i.e., roll) stability
      - dihedral effect
      - wings pointing upward increase the angle-of-attack of the lower wing due in turn-induced sideslip, rolling it back
  - general properties
    - an inherently stable aircraft will require less effort to control
  - great figures:
    - https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/aircraft-stability-control/
    - https://en.wikipedia.org/wiki/Longitudinal_stability
Center of pressure (CG )vs center of Gravity
- CP MUST aft of the CG to ensure longitudinal stability, i.e. order from prop to tail is
  - Alphabetical order (E, G, P, S ~ engine, center of Gravity, center of Pressure, Stabilizer)
  - Engine (nose-heavy weight pointing downward)
  - CG (pivot point)
  - CP (center of pressure pointing up) = Aerodynmic Center = Center of Lift
  - horizontal Stabilzer (producing downward lift, acting as an inverted wing)
- imagine
  - aircraft is in trimmed flight
  - nose-up disturbance is triggered
    - nose goes up
    - angle of attack increases
    - lift increases and rotates the CP up around the CG back to level
  - or nose-down disturbance is triggered
    - nose goes down
    - angle of attack increases
    - lift decreases and releases the CP down around the CG back to level
- summary
  - thus, if CG is too far aft and gets too close to the CP we lose static stability
  - if CG even gets behind the CP, the aircraft is statically unstable
CG ahead of CP: static positve stability
collocation of CG and CP: static neutral stability
CP ahead of CG: static negative stability (i.e., aggravation)
When conducting a prefligt, the PIC must use the most current weight and balance data (not just factory or recent data).

K3: Aerodynamics

four forces of flight
- in steady flight
  - forces
    - lift
    - weight
    - thrust
    - drag
      - is produced by moving the airplane through the air
      - types of drag:
        
        (lift-)induced drag
        
        the rearward retarding force by the wings creating lift
        
        highest at low speeds during high angle of attacks
        
        thus, induced drag increases when airspeed is decreased
        
        parasite drag
        
        the drag caused by the fuselage and other protrusions disprupting the flow of air
        
        increases quadratically with speed
        
        sub-types
        
        form drag
        
        general aircraft shape
        
        skin friction drag
        
        can be somewhat reduced through flush riveting, smooth paint, waxing
        
        intereference drag
        
        turbuluences from different aircraft components
  - relationship in steady flight
    - The four forces of flight in equiblibrium during unaccelerated (straigh-and-level) flight
    - In steady, unaccelerated (straight-and-level) flight,
      - lift equals weight
      - thrust equals drag
  - In straight-and-level flight, if thrust exceeds drag,
    - speed increases.
  - In a climb and in a descent, lift is less than weight
    - In a climb, lift is less than weight, and the missing part of weight is instead pulled up by thrust.
turns
- horizontal component of lift:
  - the force that makes an airplane turn
  - does explain why the aircraft moves sideways, but does not explain why the nose points in the direction of sidways motion
    - The aircraft weathervanes into the direction of the turn
- standard rate of turn
  - turn rate of 3° per second, thus
    - 180° / 3 °/s = 60 seconds for a 180-turn
    - 2 minutes for a 360-turn
- centripetal and centrifugal forces:
  - centripetal force: real inward-pulling force in a turn
  - centrifugal (mnemonic "f" = fictious) force: fictious force sensed as outward pulling force in a turn
- induced by cross-controlled aileron deflection 1) turn yoke to the left 2) left aileron deflects up (thump up points to aileron up), right aileron deflects down 3) left aileron reduces wing's angle of attack (decreasing lift), right aileron increases wing's angle of attack (increasing lift) 4) lift increase raises right wing, but also increases lift-induced drag 5) drag yaws aircraft to raised wing (adverse yaw) 6) left rudder needed to correct for adverse yaw
the movement of the air affects the speed at which aircraft move over the earth's surface
- i.e., wind speed affects ground speed, not true airspeed
lift
- lift equation
  - lift = lift coefficient x density x (v^2)/2 x wing area
- jointly produced by two principles
  - Newton's third law
    - For every action, there is an equal and opposite reaction
    - In the airplane context: An additional upward force is generated as the lower surface of the wing deflects air downward.
  - Bernoulli's principle
    - Air traveling faster over the curved upper surface of an airfoil causes lower pressure on the top surface.
- lift coefficient encodes the angle of attack
  - angle between
    - oncoming air / relative air flow and
    - the wing's/airfoil's chord line
- effects of frost on lift
  - disrupts the airflow, thus decreasing lift
  - spoils the smooth flow, thereby decreasing lifting capability
  - may prevent the airplane from becoming airborne at normal takeoff speed
- wing design properties
  - top-down view: swept wings vs tapered vs rectangular design
  - front view: dihedral design to ensure the aircraft rolls back
  - side view: wing twists (higher angle of attack at the root) and stall strips to ensure the wing root stalls first and the ailerons remain effective until last
aircraft categories
- normal: +3.8 to -1.52
- utility (incl. spins): +4.4 to -1.76
- aerobatic: +6.0 to -3.00
T-tail aircraft
- deep stall
  - conditions
    - high AOA
    - low airspeed
    - aft CG
  - principle
    - tail is blanketed by airflow, rendering elevator unusable
  - results
    - uncrecoverable stall
    - no elevator buffetting
propeller aerodynamics
- reducing power reduces the slipstream/downwash effect on the elevator, thus stops pressing down the elevator and therefore ontroduces a pitchdown moment
- left-turning tendencies
  - slipstream
    - downwash spirals over the fuselage and empennage hitting the left side of the vertical stabilizer, creating a yaw to the left
    - most pronounced during low-speed, high power setting (e.g., during takeoff), where the slipstream is most of the produced air
  - asymmetric propeller loading (p-factor)
    - seen from the cockpit, in the US, the propeller turns clockwise, meaning
      - the descending blade is on the right side
      - the ascending blade is on the left side
    - this means, during a high pitch up attitude (even imagine a helicopter in the extreme case)
      - the descending blade moves down-forward in the direction of the flight path
      - the ascending blade moves up-backward against the direction of the flight
    - this means, oncoming air over the
      - the descending blade is the sum of aircraft speed and propeller speed
      - the ascending blade is the difference between aircraft and propeller speed (much lower than on the descending speed)
    - this means the descending blade creates more lift (we call it thrust for the propeller)
  - torque
    - newton’s third law that states "for every action, there is an equal and opposite reaction"
    - idea: the engine turns the prop clockwise (seen from the cockpit), or the prop turns the engine counterclockwise
    - highest at low airspeed, high power, high angle of attack
    - pushes left landing gear down during takeoff roll
  - gyroscopic precession
    - mechanis
      - an applied force appears 90 degrees ahead in the direction of rotation
    - effect:
      - pitching the nose up or down produces a force on the right side, esp. during take-off right rudder is required
rudder use cases:
- correct left-turning tendencies
- correct adverse yaw
- slips (forward slips, side slips)

Risk

R1: Use of performance charts, tables, and data

R2: Airplane limitations

R3: Possible differences between calculated performance and actual performance

Skills

S1: Compute the weight and balance, correct out-of-CG loading errors, and determine if the weight and balance remains within limits during all phases of flight