Additional Math Pages & Resources

Monday, August 17, 2009

Airplane Math

You can't be a pilot without also being good at math. Numbers, numbers, numbers.

Pilots worry about how much weight an aircraft can carry, how long a runway it needs to take off and land, how far it can fly and how fast it can fly.

For instance, let's look at weight. The weight of an aircraft is the total of:

1. Plane (operational weight empty, includes pilot)
2. Fuel (usable fuel & reserve fuel)
3. Passengers & cargo (payload)

The plane I flew on this weekend was a CRJ700 regional jet.

1. Plane Empty = 43,500 lbs
2. Maximum Fuel = 19,500 lbs
3. Maximum Payload with full fuel = 10,500 lbs or with less fuel = 18,800 lbs
4. Maximum Take-off Weight = 72,750 lbs

Maximum Take-Off Weight = Plane Empty + Fuel + Payload.

Notice that Fuel and Payload are variables we can adjust to stay under the Maximum Take-Off Weight. Now that we know this - we can ask "How many passengers can this plane carry?"

The FAA tells us to use these weights:
  • Women 179-184 lbs. (including clothes & carry-on)
  • Men 200-205 lbs. (including clothes & carry-on)
  • Checked bag 30 lbs.
Let's assume equal numbers of men and women, with one bag per person. How many can we carry and still stay under Maximum Take-Off Weight? Here's one way to find the answer:

180 + 200 = 380 ÷ 2 = average 190 lbs per person then add 30 for a bag to get 220 lbs.

Maximum payload of 18,800 ÷ 220 = 85 people.

Since this plane seats 70 plus a crew of 4, it looks like we have a bit of excess capacity. Of course flight distances can be limited if we can't carry a full load of fuel. And we have to consider that
  • If we have bad weather or delays we need more fuel so we can't carry as much payload.
  • If the weather is hot we need more runway to take off or less payload.
  • If the airport is above sea level it also means more runway or less load.
Let's stop there. Whew! Math can be hard mental work.

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