Density altitude

Hot and high factors shorten runways with summer and mountain flying.

By Karsten Shein
Comm-Inst, Climate Scientist

Runway 33 at ASE (Aspen CO) on a sunny early fall day. At 7820 ft MSL and with rising terrain on liftoff, many pilots have gotten into density altitude trouble at airports such as this.

Tom watched with dismay as the boss and his buddies began to toss the heavy-looking gear bags in the back of the aircraft. This was just supposed to be a weekend hunting trip, but these guys had enough gear to storm the beach at Normandy.

Next came the coolers, no doubt full of game meat, judging by the grunting of the 2 strong fellows hefting them to­ward the cargo hatch. It was midday and temperatures at this high mountain airport were already pushing 80°F.

Tom was worried about the turboprop’s weight and balance, but didn’t dare say anything since he was a relatively new hire and he had heard that the previous pilot had been fired over his refusal to fly through a strong cold front to get his boss to a meeting on time.

Just before throttling up at the end of the 8000-ft strip, Tom glanced back at the hefty executives, each over 200 lbs, and thought about the coolers, which must have weighed at least 300 lbs apiece. This would not be a relaxing flight.

He had already anticipated the difficulties getting out of this backcountry airport and had arrived with just enough fuel to make the short hop out of the mountains to a lower-altitude airport. Unfortunately, that meant that an aborted takeoff would leave him short on fuel. In assessing the lesser of 2 evils, Tom chose to risk the potential of a density altitude accident over the certainty of an out-of-fuel one.

The turboprop screamed forward, but gathered pace much more slowly than usual. Tom hit V1 and acceleration seemed to stop just short of Vr, so he tried to break the airplane into ground effect as the runway end approached.

With about 100 ft of runway left—and only around Vr rather than the V2 he had hoped for—he rotated and the aircraft began to rise. As expected, the climb was sluggish, and Tom quickly realized that he wasn’t going to clear the trees on the rising terrain ahead.

As his options evaporated, Tom banked toward a small gully but, with his climb attitude and low speed he stalled and dropped his wing into the trees, becoming yet another density altitude accident statistic in the NTSB files.

Unfortunately, Tom’s situation, while fictional, is not an unrealistic scenario. In fact, video from an eerily similar situation involving a Cessna L19E that crashed in near Tabernash CO in Aug 1992 is posted on YouTube (at youtube.com/ watch?v=ZfPr_gZzHRw).

Job constraints, a lapse in judgment, get-home-itis, or any number of other factors can lead experienced pilots to shave safety margins from their flight and operate near the razor edge of the aircraft’s operational envelope.

Sometimes, however, pilots miscalculate and find themselves well outside that envelope with no recourse. Density altitude is one of those situations that, because it is invisible to us and generally affects us most when the flying weather is otherwise optimal, is easy to ignore. But ignoring it is ignoring the basic physics that allows our aircraft to fly in the first place.

With summer in the Northern Hemisphere nearly upon us, most of us will be preparing to deal with severe summer weather. In addition, those of us who regularly fly out of smaller high-altitude airports will undoubtedly be brushing up on the density altitude and MTOW limitations of our aircraft.

It’s the rest of us, who visit these airports only occasionally, for whom awareness of density altitudes is perhaps most critical.

Aerodynamics 101

DEN (Intl, Denver CO) airport diagram. With a field elevation of 5431 ft, the “Mile High” airport can be prone to significant adverse density altitudes in summer.

In large part, the success of the Wright Brothers’ Flyer was due to the aerodynamic experiments they and their contemporary Samuel Langley had conducted on wing shapes.

Like German glider inventor Otto Lilienthal before them, they understood the concept that a lifting force would be generated when the pressure beneath an object exceeded the pressure above it.

This aerodynamic relationship had been known for centuries, but the Wrights were among the first to prove it with wind tunnel experiments. The lift generated by an airfoil is tied fundamentally to what is known as Bernoulli’s Principle.

In the early 1700s, Daniel Bernoulli discovered that, as an incompressible fluid such as water is forced to flow through a smaller diameter pipe, its velocity increases and the pressure decreases.

Since air moving at sub-Mach speed is considered an incompressible fluid, as it flows over a curved surface it is in effect being forced to move through a smaller-cross-section area bounded by more air above and the wing surface below.

So, to compensate, the flow speed increases and the molecules in the air spread out, lowering the pressure. Of course, the curvature of airfoils also directs trailing air downward, increasing lifting forces, but the pressure differential between the top and bottom of the airfoil is the key to lift.

So what does this have to do with density altitude? The amount of lift an airfoil generates is a function of a simple equation—force equals mass times acceleration times area. The downward force generated by gravity must be overcome by an upward force created by airflow over the wing.

Since the area is fixed, we can only change the mass or acceleration. Fortunately, air has mass. We feel it in the force of the wind blowing against our faces. Air is nothing more than a bunch of gas mole­cules such as nitrogen, oxygen and water vapor. Each of these mole­cules has a tiny bit of mass, which collectively can be sufficient to drive the lifting force.

However, a cubic meter of air has a mass of just about 1.2 kg and no ability to generate a pressure differential between the top and bottom of a wing. To get that 1.2 kg of air generating enough lift to overcome gravity, we must move the air past the airfoil at a sufficient speed.

Because the lift force is dependent on the mass of air molecules in a given space, any change in that mass will result in a change in the lifting force. This is where air density comes in. Air density is that mass (often thought of as the number of molecules) per unit volume.

If air density decreases, the only way to keep the lifting force steady is to increase the flow of air across the airfoil. Increases in speed are a function of aircraft thrust, which itself is dependent on air density.


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