Density Altitude at Canyon Ridge
A pilot plans a departure from Canyon Ridge Airport, elevation 5,200 feet MSL, on runway 27: 3,200 feet of dry asphalt with 40-foot trees about 200 feet beyond the departure end. The airplane is a Cessna 172S loaded to its 2,550-pound maximum gross weight with two adults (340 pounds), 40 pounds of baggage, and full fuel. The altimeter setting is 30.02 inHg and the surface temperature is 32 °C (about 90 °F); wind is calm. The pilot's takeoff chart (full throttle, flaps 0, no wind) shows: at 5,000 feet pressure altitude and 30 °C, ground roll 1,425 feet and total distance over a 50-foot obstacle 2,640 feet; at 8,000 feet and 30 °C, ground roll 2,010 feet and total over 50 feet 3,750 feet. Terrain rises about 1,200 feet within 5 miles of the departure end, and the airplane's best rate of climb at this weight is already modest. The only alternative is a 0630 departure, when the temperature is forecast to be 14 °C.
1. Compute the pressure altitude and density altitude for the planned 32 °C departure, and explain what each number represents.
Read the worked answer
Pressure altitude corrects field elevation for the nonstandard altimeter setting:
PA = field elevation + (29.92 − altimeter) × 1,000 PA = 5,200 + (29.92 − 30.02) × 1,000 = 5,200 − 100 = 5,100 ft
Because the altimeter setting is above 29.92, the airplane is sitting lower in the atmosphere than the elevation suggests.
Density altitude corrects pressure altitude for temperature. Standard temperature at 5,100 ft is about 15 − (2 × 5.1) ≈ 4.9 °C. Using roughly 120 ft per degree Celsius of deviation:
DA ≈ 5,100 + 120 × (32 − 4.9) = 5,100 + 3,252 ≈ 8,350 ft
The airplane will perform as though it were taking off at 8,350 feet even though the runway sits at 5,200. That is the number that drives every performance decision: the engine produces less power, the propeller produces less thrust, and the wing needs a higher true airspeed for the same indicated lift - so the ground roll lengthens, the climb rate drops, and the obstacle clearance shrinks.
2. Interpolate the takeoff chart for the planned departure and decide whether it can be made. What margin is acceptable?
Read the worked answer
8,350 ft is 3,350 ft above the 5,000-ft chart row, i.e., 3,350/3,000 = 1.12 of the way to the 8,000-ft row.
- Ground roll: 1,425 + 1.12 × (2,010 − 1,425) = 1,425 + 655 ≈ 2,080 ft
- Over a 50-ft obstacle: 2,640 + 1.12 × (3,750 − 2,640) = 2,640 + 1,243 ≈ 3,880 ft
Available distance is the 3,200-ft runway plus roughly the 200 ft to the trees, about 3,400 ft to reach 50 ft above the tree tops - and that assumes the ground past the runway end is flat and the trees are the only obstacle.
The chart requires about 3,880 ft. That is roughly 480 ft short, and the chart is already optimistic: it is flown by a test pilot in a new airplane with a fresh engine. Add 50 percent for a rental with an average engine and a low-time pilot and the required distance is nearer 5,800 ft.
Decision: no-go at max gross and 32 °C. There is no margin at all, and the rising terrain means a sluggish climb is not recoverable by simply lowering the nose. Even a chart value 20 percent under the available distance would be thin for a high-altitude departure into rising terrain.
3. What combination of changes would make this departure defensible, and what would you check in the airplane before accepting the plan?
Read the worked answer
The two controllable variables are temperature and weight.
Temperature. At 14 °C, standard temperature at 5,100 ft is 4.9 °C, so DA ≈ 5,100 + 120 × (14 − 4.9) ≈ 6,200 ft. That is 0.40 of the way from the 5,000-ft row to the 8,000-ft row: ground roll ≈ 1,660 ft, over 50 ft ≈ 3,080 ft. Against 3,400 ft available, that is a margin of about 320 ft - better, but only about 10 percent, which is still inside the slop of a book number versus a real airplane.
Weight. Offloading fuel and baggage is the second lever. Cutting 20 gallons (120 lb) and the 40 lb of bags removes about 160 lb, and in this class of airplane that trims takeoff distance by roughly 8–10 percent per 100 lb - verify with the POH weight-correction chart rather than a rule of thumb. Combining the cool morning with 25 gallons aboard and no baggage brings the required distance to roughly 2,600–2,800 ft, which is a real margin.
Before accepting the plan, check: actual weight and balance, not assumed; the POH chart for the exact pressure altitude, temperature, and weight with the grass/wet correction if applicable; density altitude at the time of departure, not a forecast from an hour earlier; the climb gradient needed to clear the rising terrain versus the chart's rate of climb; and a decision point - abort if the airplane is not at 70 kt and climbing by midfield, and turn away from high terrain rather than trying to out-climb it.