Study guide
Weather sets the conditions you fly in, and weight and balance combined with performance data determine whether a given flight is even possible on a given day. This chapter reviews atmospheric behavior and report interpretation, then walks through three fully worked calculations, each solved twice, covering density altitude, weight and balance, and takeoff performance interpolation.
Atmospheric Stability, Fronts, and Hazards
Atmospheric stability describes whether a displaced parcel of air tends to return to its original level, stable air, or continues rising on its own, unstable air. Stable air tends to produce smooth flight, stratiform clouds, steady precipitation, and haze or fog, while unstable air produces turbulence, cumuliform clouds, showery precipitation, and good visibility away from showers. A front is the boundary between two air masses of different temperature and moisture characteristics. A cold front, where cold air displaces warm air, tends to move quickly and can produce a narrow band of intense weather including thunderstorms, gusty winds, and rapid clearing behind it. A warm front, where warm air overtakes and rises over cold air, tends to move more slowly and produce widespread stratiform clouds, extended periods of steady precipitation, and lower ceilings and visibility well ahead of the surface front. Thunderstorms require three ingredients: sufficient moisture, an unstable lapse rate, and a lifting mechanism, and a mature thunderstorm cell can produce severe turbulence, hail, lightning, heavy rain, and a gust front of rapidly shifting surface wind; airplanes should avoid thunderstorm cells by a wide margin and should never attempt to fly through or under one. Icing is a serious hazard for a non-deiced training airplane and requires visible moisture, such as clouds or precipitation, and temperatures near or below freezing; structural ice on the wings, especially disrupting airflow over the leading edge, degrades lift and increases stall speed, so pilots avoid known icing conditions rather than attempt to fly through them.
Reading METAR, TAF, and Weather Briefings
A METAR is a routine surface weather observation issued hourly, or more often when conditions change significantly, formatted in a standardized code. A typical METAR reports the station identifier, the day and time in coordinated universal time, wind direction and speed, visibility in statute miles, present weather, sky condition by cloud layer height and coverage such as few, scattered, broken, or overcast, temperature and dew point in Celsius, the altimeter setting, and sometimes remarks. A close spread between temperature and dew point suggests air is near saturation and fog or low clouds are more likely. A TAF, terminal aerodrome forecast, uses similar coded language to forecast conditions at an airport for a set period, typically 24 to 30 hours, and includes expected changes introduced by terms describing gradual or rapid transitions. Before a cross-country flight, pilots review a weather briefing that synthesizes current METARs, TAFs, area forecasts, AIRMETs covering hazards such as moderate icing, moderate turbulence, and widespread mountain obscuration, and SIGMETs covering more severe hazards including severe icing, severe turbulence, and dust storms, along with any pilot reports from aircraft already in flight. A pilot named Grace planning a Saturday morning flight would check the departure, en route, and destination METARs and TAFs together, since a clear departure airport does not guarantee a usable destination if a warm front is forecast to arrive by early afternoon.
Weight and Balance Fundamentals
Every aircraft has published weight and balance limits: a maximum gross weight it must not exceed, and a center of gravity range, expressed as a distance from a reference datum, within which the loaded aircraft's balance point must fall. Operating outside either limit is a regulatory violation and a safety hazard, since an aft center of gravity can make an airplane less stable and harder to recover from a stall, while excess weight degrades climb performance and increases stall speed and landing distance. Weight and balance calculations use three related values: weight, the force an item exerts; arm, the horizontal distance from the datum to the item; and moment, the product of weight multiplied by arm, which represents that item's turning effect around the datum. To find an aircraft's loaded center of gravity, a pilot lists the weight of the empty aircraft and each item added, such as pilot, passengers, fuel, and baggage, multiplies each weight by its arm to get its moment, sums all the weights and sums all the moments separately, and divides total moment by total weight to get the center of gravity in inches from the datum. That resulting CG value is then compared against the aircraft's loading envelope, a graph or table showing the acceptable combination of weight and CG, to confirm the loaded aircraft falls inside the approved range at both the current weight and the anticipated landing weight after fuel burn.
Worked Calculation: Weight and Balance
Consider a training airplane with a basic empty weight of 1,467 pounds and an empty-weight moment of 100,655 inch-pounds. The pilot and front passenger together weigh 340 pounds at a front-seat arm of 37 inches. A rear passenger weighs 300 pounds at a rear-seat arm of 73 inches. Fuel is loaded at 40 gallons, which at 6 pounds per gallon equals 240 pounds, at a fuel-tank arm of 48 inches. Baggage weighs 50 pounds at a baggage-compartment arm of 95 inches. First pass: multiply each weight by its arm to find its moment — front seats, 340 times 37 equals 12,580; rear seat, 300 times 73 equals 21,900; fuel, 240 times 48 equals 11,520; baggage, 50 times 95 equals 4,750. Add all weights: 1,467 plus 340 plus 300 plus 240 plus 50 equals 2,397 pounds. Add all moments: 100,655 plus 12,580 plus 21,900 plus 11,520 plus 4,750 equals 151,405 inch-pounds. Divide total moment by total weight: 151,405 divided by 2,397 equals approximately 63.16 inches aft of the datum. Second pass, recomputed independently to confirm: weights again sum to 2,397 pounds; moments again sum to 151,405 inch-pounds; 151,405 divided by 2,397 again yields 63.16 inches. If this airplane's approved envelope allows a maximum gross weight of 2,400 pounds with a CG range of 35 to 88 inches at that weight, this loading is within limits on both counts, with only 3 pounds of weight margin remaining.
Worked Calculations: Density Altitude and Takeoff Performance
Density altitude affects engine power, propeller efficiency, and lift, so pilots calculate it before every performance-limited takeoff. Example: field elevation is 3,200 feet, the altimeter setting is 29.92, so pressure altitude equals field elevation at 3,200 feet, and the outside air temperature is 30 degrees Celsius. First pass: standard temperature at 3,200 feet equals 15 degrees Celsius minus 2 degrees for each 1,000 feet, or 15 minus 6.4, equal to 8.6 degrees Celsius. The deviation from standard is 30 minus 8.6, equal to 21.4 degrees. Density altitude equals pressure altitude plus 120 feet for each degree of deviation: 3,200 plus, 120 times 21.4, equal to 3,200 plus 2,568, equal to 5,768 feet. Second pass, recomputed: standard temperature again 8.6 degrees Celsius, deviation again 21.4 degrees, density altitude again 3,200 plus 2,568 equals 5,768 feet, confirmed. Now a takeoff distance interpolation: a performance chart lists, at a pressure altitude of 2,000 feet and 20 degrees Celsius, a ground roll of 1,000 feet and a total distance over a 50-foot obstacle of 1,800 feet; at the same pressure altitude and 30 degrees Celsius, ground roll is 1,100 feet and total distance is 1,975 feet. For an actual temperature of 25 degrees Celsius, halfway between the two chart temperatures, interpolate: ground roll equals 1,000 plus, 1,100 minus 1,000, times, 25 minus 20 divided by 30 minus 20, equal to 1,000 plus 50, equal to 1,050 feet; total distance equals 1,800 plus, 1,975 minus 1,800, times one-half, equal to 1,800 plus 87.5, equal to approximately 1,888 feet. Second pass, recomputed: the temperature fraction is again exactly one-half, so ground roll again equals 1,050 feet and total distance again equals approximately 1,888 feet, confirmed. A prudent pilot then adds a safety margin beyond the charted total distance before committing to a short or obstructed runway.
Key terms
- Stable air
- — Air that resists vertical displacement and tends to return to its original level, associated with smooth flight and stratiform clouds.
- Cold front
- — A fast-moving boundary where cold air displaces warm air, often producing a narrow band of intense, short-lived weather.
- Warm front
- — A slow-moving boundary where warm air rises over cold air, producing widespread stratiform clouds and extended precipitation.
- METAR
- — A coded routine surface weather observation reporting wind, visibility, sky condition, temperature, dew point, and altimeter setting.
- TAF
- — A coded terminal aerodrome forecast predicting conditions at an airport over a set future period, typically 24 to 30 hours.
- AIRMET / SIGMET
- — Inflight weather advisories for hazards to aircraft — AIRMETs cover moderate hazards, SIGMETs cover more severe hazards such as severe icing or turbulence.
- Center of gravity (CG)
- — The point along an aircraft's length, measured from a reference datum, where its total weight is considered to act.
- Moment
- — The turning effect of a weight around the datum, calculated by multiplying that weight by its arm.
- Loading envelope
- — A chart or table showing the combinations of weight and center of gravity within which an aircraft may legally be operated.
- Density altitude
- — Pressure altitude corrected for non-standard temperature, representing the altitude the aircraft's engine and wing effectively experience.
- Pressure altitude
- — The altitude indicated when the altimeter is set to 29.92 inches of mercury, used as the baseline for performance calculations.
- Interpolation
- — The method of estimating a value that falls between two known values listed on a performance chart.
Exam tips
- Redo every weight-and-balance and performance calculation a second time by an independent path before trusting the answer, exactly as shown in the worked examples.
- Memorize the density altitude rule of thumb: roughly 120 feet added per degree Celsius above standard temperature at a given pressure altitude.
- When interpolating a performance chart, find the fraction of distance between the two known columns first, then apply that same fraction to every value in the row.
- In a METAR, check temperature and dew point spread as an indicator of fog or low-cloud risk, since a narrow spread points toward saturation.
- On weight and balance questions, compute total moment and total weight separately before dividing, and double-check that arms were measured from the same reference datum throughout.