Airplane Math

by Math 4
4th Grade Math is practicing their multiplication and division skills. We decided to make some problems that NASA Mission Planners might need to work out.

NASA Airborne Research has a variety of airplanes that they use for Earth Science research. These planes are like flying laboratories and observation posts. The chart below gives some information about some of the aircraft used in missions we’ve been following this year. We are using this data to create interesting multiplication and division problems.

*	*	*
Global Hawk UAV	DC-8	P-3 Orion
12,000 lbs of fuel	160,000 lbs of fuel	60,000 lbs of fuel
30 hours flight duration	12 hours flight duration	14 hours flight duration
Take-off Weight: 25,600 lbs	Take-off Weight: 340,000 lbs	Take-off Weight: 135,000 lbs
1900 lb payload	30,000 lb payload	14,700 lb payload
397 mph	518 mph	460 mph
12,658 mile flight range	6214 mile flight range	4373 mile flight range
65,000 ft max altitude	41,000 ft max altitude	32,000 ft max altitude
Humans: 0 (UAV)	Humans: 50	Humans: 24
Missions: HS3, ATTREX	Missions: OIB	Missions: Discover-AQ
Flights: 9	Flights: 23	Flights: 10
*	*	*

Our first problem: How much fuel does each plane use in one hour of flight?

View from P-3 Orion
Discovery-AQ Flight

Discovery-AQ Scientists
Sally Pusede (l) and Kaitlin Duffey (r) on board NASA P3 Orion
photo courtesy K Duffey

Discover AQ Chat

We got to chat with scientists and mechanics onboard the P3 Orion during its mission flight to learn more about it.

eschaller: Hi Michael, welcome!

mwmathsci: Hi Emily! Photo from runway loooks like beautiful weather out there. My 4th grade math class just started their work using aircraft data.

eschlaller: It is nice here in Palmdale! We have several scientists who are onboard the P-3 right now on the chat.

mwmathsci: My students have some quesitons to pass along...
How many hours can the planes fly before engine service?
How long does routine engine service take?
What is the life of the engines?
How many flights can a plane take becore it “wears out”?

sally_P3B: hi everyone! my name is Sally and I’m a scientists on the P3. Those are great questions, they are best answered by the flight crew. let me ask.

sally_P3B: ok, Todd, an AP mechanic and flight crew member, is explaining the answers to me (I’ll type though).
He say: engines get serviced annually. We fly them until they fail. Engine service takes just a day or two to do all 4 engines. 7 mechanics work on the annual service. There is also non-routine maintanence to do too. Engines aren’t the only thing that needs maintenance.

sally_P3B: our plane was made in 1965

mwmathsci: Wow! That plane is as old as our teacher!

sally_P3B: haha

mwmathsci: What does Todd like best about his job? What’s the hardest part?
sally_P3B: He says he loves every part of his job! The hardest part is being away from home for long missions.

mwmathsci: How many hours has the P3 logged for NASA?
sally_P3B: actually this P3 has already flown more than 20,000 hours. But they have engineered it so that it has an extra long life.

mwmathsci: We did some calculations today and figured out the P3 uses about 4286 lbs of fuel per hour. How’d we do?
sally_P3B: you did great! Todd says just under 5000 lbs. All the instruments on the plane make it weigh more, so it uses extra fuel. It also has more drag.

mwmathsci: Why more drag?
sally_P3B: You all have such great questions!

mwmathsci: Thanks. I think I have some future aviators, logistics and mission ops peeps here.
sally_P3B: the extra drag comes from all the instruments and the modified fairing (this is the shape of bottom of the plane)

mwmathsci: How much safety reserve does the mission plan for?
sally_P3B: The safety reserve is an extra 10,000-12,000 lbs of fuel.

mwmathsci: What science are you doing? What are you measuring on this flight?
sally_P3B: we are measuring many different gas molecuels including carbon monoxide (CO), carbon dioxide (CO2), ozone (O3), nitrogen dioxides (NOx = NO + NO2). As well as particles, including particle concentration, size, shape, interaciton with light, and composition.

mwmathsci: different kinds of pollution?
sally_P3B: yes, the gasious chemicals are all very important pollutants. Especially in the Central Valley of California where the air pollution is very bad. We also measure meteorological parameters such as wind speed and wind direction, temperature, etc.

mwmathsci: can you tell the difference between “natural” and human sources?
sally_P3B: sure! Human sources - sometimes called anthropogenic sources - are any source that comes directly from a human-made source, or is influenced, for example by chemical reactions, by human made sources. In the atmosphere it is not always easy to determine human from natural sources. But in many cases molecules are uniquely one or the other. This is why it is important to measure many different chemicals at the same time.

mwmathsci: Thanks Emily, Sally and Todd! We have to go to lunch now.