Leadville on a July Afternoon: Density Altitude and a Chart That Ends at 10,000 Feet
Dana, a 130-hour private pilot, plans to fly her family from Lake County Airport, Leadville, Colorado (elevation 9,934 ft MSL) to Salina, Kansas, in a club Cessna 172S (Lycoming IO-360, 180 hp, maximum gross weight 2,550 lb, 56 gallons usable, empty weight 1,680 lb). Runway 34 is 6,400 ft of asphalt with rising terrain to the north. The forecast for a 1 p.m. departure: temperature 24 °C, altimeter 30.12, wind 220 at 8, sky clear. Load: Dana 145 lb, her husband 210 lb, two children 95 lb each, 60 lb of bags, and full fuel. She has read 1,900 ft of takeoff distance off the POH chart at 10,000 ft pressure altitude and 20 °C and says, "we have three times that much runway." The POH performance charts stop at 10,000 ft pressure altitude. She asks the club's ground instructor whether her numbers are good.
1. Work out the density altitude for this departure and explain what it does to the airplane, not just what the number is.
Read the worked answer
Pressure altitude: 9,934 + (29.92 − 30.12) × 1,000 ≈ 9,730 ft.
Standard temperature at that altitude: roughly 15 − (1.98 × 9.73) ≈ −4 °C.
Density altitude: 9,730 + 120 × (24 − (−4)) ≈ 9,730 + 3,360 ≈ 13,100 ft.
Why it matters. The airplane behaves as if it were sitting at 13,100 ft on a standard day, which is close to its service ceiling. Three consequences stack up:
- Less power. A normally aspirated engine loses roughly 3 percent of sea-level power per 1,000 ft of density altitude. At 13,100 ft that is on the order of a quarter of rated output gone before the throttle is even fully open.
- Higher true airspeed for the same indicated airspeed. The wing needs a higher groundspeed down the runway to reach flying speed, so the ground roll stretches far beyond the chart value.
- Weaker climb. Excess thrust is what climbs, and it is the first thing to disappear. Expect a few hundred feet per minute at best, and less once the airplane is leaned and hot.
Dana's 1,900-ft figure was read at a density altitude more than 3,000 ft below the actual condition.
2. Dana's argument is that 6,400 ft of runway is three times what she needs. Explain why runway length does not settle this, and identify the second problem with her loading that she has not checked.
Read the worked answer
Runway length only answers the first third of the question. It tells you whether the airplane can accelerate and lift off. It says nothing about whether it can out-climb the rising terrain to the north, and nothing about what happens if an engine falters at 200 ft with a ridge ahead. On a 13,100-ft density altitude day, obstacle clearance - not ground roll - is the binding constraint. A long runway can actually make the problem worse by tempting a departure that should not happen at all.
The chart extrapolation problem. Her number came from 10,000 ft and 20 °C. The actual condition is 3,000 ft of density altitude beyond the last line on the chart. Performance charts are not linear beyond their published limits, and interpolating or extrapolating off the edge is not a valid planning method; the correct answer off the chart is "unknown," and unknown is a no-go.
The weight problem. Empty 1,680 + 145 + 210 + 95 + 95 + 60 + 336 (full fuel) = 2,621 lb. That is 71 lb over the 2,550-lb maximum gross weight before anyone has started the engine. Over gross adds to both takeoff distance and climb penalty, compounding the density altitude problem.
3. Name two changes that would make this departure realistic, and explain how you would teach the go/no-go decision inside the cockpit.
Read the worked answer
Changes that actually move the numbers:
- Depart at dawn. At 8 °C instead of 24 °C the density altitude drops by roughly 1,900 ft. That single change does more than any other.
- Take less fuel and buy it downhill. Twenty gallons less removes 120 lb - enough to fix the gross-weight problem and reduce the climb penalty. Fuel is cheap at lower elevations; margin is not.
- Leave a passenger or the bags behind, or split the family across two airplanes.
Teaching the decision. The value is in deciding before taxi, not over the trees.
- Pick a physical abort point on the runway (a taxiway intersection, a runway distance marker) and a speed by which the airplane must be indicating a specific value or the takeoff is rejected.
- Before departure, brief a minimum climb rate and a maximum altitude-loss tolerance; if the airplane cannot hold it by pattern altitude, return and land.
- Brief the terrain escape: which way to turn, at what altitude, and where the nearest suitable runway is.
- Say the go/no-go out loud as a crew briefing, so the decision is made once, calmly, rather than renegotiated in the air as the ridge gets closer.