Keeping Track of Kuiper: Background Information

Stefan has provided data sets from two flights of the Kuiper Airborne Observatory (KAO) that included the altitude, latitude, longitude, cabin pressure, outdoor pressure, and outdoor temperature for the duration of each flight. This data is saved in an Excel Spreadsheet and can be easily manipulated to create the graphs presented in this lesson. These graphs allow students 1) to become familiar with the characteristic flight profile of the KAO, and 2) to learn about the relationship between pressure, temperature, and altitude. For the purposes of this lesson, the KAO served as a atmospheric probe of both temperature and pressure.

Because the KAO is an Airborne Observatory conducting infrared astronomy, the bulk of the flights take off in the evening just before or after sunset (local pacific time), though a few of the flights (engineering or checkout flights) are earlier in the day. Graphs show time as universal time in an hh:mm:ss format. Universal Time is 7 hours ahead of Pacific Standard Time. Most flights are about 7.5 hours in duration, with a corresponding 7 hours between the ascent and the descent profiles, though some are shorter (either due to the flight plan, aborted missions post-takeoff, or engineering flights).

NOTE: Flight data from the middle of each flight (when the aircraft was at 41000 ft) has been removed to make the files more manageable in size. Also, this data is preliminary, raw data taken directly from sensors on the airplane. Slight variations due to airspeed, angle of attack, and other factors may occur.

Keeping Track of Kuiper: General Features to Notice in Graphs

Below is a brief description of each of the graphs along with some special notes about analyzing each graph. Use these comments as background for preparing your lesson. A sample worksheet based upon the data is also attached.

Also, note that each graph is presented twice, once for the 5/4/94 flight and once for the 6/3/94 flight. Students can learn a lot by comparing graphs from different flights. Was air pressure the same at 35000 feet on both days? Was air temperature the same at 20000 feet on both days? Did the airplane fly for the same amount of time on both days? Did it take off at the same time? etc.??!

KAO Flight Profile

1. This graph plots time on the bottom (Universal Time) and altitude on the side (feet). Universal Time is 7 hours ahead of Pacific Standard Time. The format for time is hh:mm:ss.

2. This graph shows the airplane taking of, climbing to one or two initial cruising altitudes, and eventually reaching a cruising altitude of 41000 feet. The KAO typically holds at about 37000 feet to burn off enough fuel so that it can more efficiently reach its maximum cruising altitude of 41000 feet.

3. Both ascent and descent take about 30 minutes each, with a 7 hour flight in-between in which astronomy is (hopefully) carried out.

4. Compare and contrast the Flight Profiles for both flights (5/4/94 and 6/3/94). They are now identical. Why?

KAO Ascent Profile

1. This graph plots time (UT) on the bottom, altitude (feet) on the left axis, and pressure (atm) on the right axis. Note that diamond-shaped altitude data points correspond to the left axis, and box- and triangle-shaped pressure data points correspond to the right axis.

2. Note that outside pressure drops from around 1.0 atm at sea level down to 0.24 atm at 41000 feet. Cabin pressure, on the other hand, does not drop as much (fortunately!!). The cabin is pressurized to around 0.76 atmospheres when the plane is at 41000 feet. Note that a pressure of 0.76 atmospheres is equivalent to the outside pressure when the airplane is at 10000 feet. Hence, the cabin is pressurized to an altitude equivalent to 10000 feet.

3. Whenever the KAO levels off, the pressure levels off, showing that pressure is constant at a given altitude.

KAO Descent Profile

1. This graph has the same format as the Ascent Profile graph above, except that it is shows the KAO landing instead of taking off.

2. Note the relationship again that outdoor pressure goes up as you get closer to the earth's surface.

3. The slope of the descent graph is not constant. In both flights, the plane quickly descends to 8000 feet and then levels off and more slowly descends to the landing strip at 0 ft.

Altitude v. Pressure - KAO

1. This graph shows outside pressure (atm) as a function of altitude (feet). The graph plots outside pressure data from both the ascent and the descent of the aircraft.

2. A good activity is to have students make their own altitude/pressure graph from the previous graphs above. You could have students do this with graph paper and pencil, or you could teach them how to use Excel and make the graphs electronically, like the one provided.

3. Note that pressures were higher for the descent than the ascent between 9000 ft and 40000 feet. This probably has something to do with the rate of descent, the use of spoilers on the airplane to slow it's descent, or other aeronautical factors. This same effect probably accounts for the changes in slope of the pressure graph. (The angle of attach and the airspeed affect pressure readings.)

4. Note the shape of the ascent data at 39000 feet, 41000 feet, and any other cruising altitudes. There is a vertical bar rather than a single point. This is again because of sampling differences. The airplane sampled air pressure for a long duration of time at these altitudes and fluctuations are obviously going to occur.

Altitude v. Temperature - KAO

1. This graph plots air temperature ('C) as a function of altitude (ft).

2. Note again vertical lines at 37000 ft, 41000 ft, and other cruising altitudes. Apparently temperature varies more than pressure as the airplane flies through a column of air at the same altitude. Different pockets of air will have different temperatures.

3. Notice that the highest temperature for descent data on both graphs is not at 0 ft. Rather, temperature peaks at 5500 ft. Notice also that it is colder between 0-3000 feet in the morning than in the evening. Notice that at higher elevations, though, it is the reverse - descent data (morning) is hotter than ascent data (evening). ARE ANY OF THESE FEATURES REAL or ARE THEY JUST MEASURING ERRORS? I (John Keller) am not sure, but I would be cautious in looking for too much detail in the data.

4. This graph is not included in the lesson below. I would probably introduce this graph to the students as follow-up activity and simply talk about what the data means.

Follow-up activities

After finishing the lesson below, I would pass out the altitude v. pressure graph and show them what the complete graph looks like and talk about the data presented.

Also, I would then pass out the altitude v. temperature graph and discuss how temperature varies with altitude.

Keeping Track of Kuiper

Introduction

The Kuiper Airborne Observatory (KAO) involves a telescope flown aboard a C-141A aircraft stationed at NASA-Ames Research Center in California. The primary mission of this aircraft is to carry out airborne infrared astronomy up above most of the water vapor in our atmosphere. Water vapor absorbs infrared radiation coming from planets/stars/galaxies. In order for astronomers to view this radiation, a telescope must be flown above this water - hence the KAO.

A secondary experiment was piggy-backed to this airborne observatory during the spring and summer of 1994. Dr. Mark Kritz and Stefan Rosner collected samples of radon gas as the airplane flew up through the atmosphere from 0 to 41000 feet as part of the Radon Vertical Profiles (RVP) Program. This data is useful for modeling concentrations and movements of air through our atmosphere - which is important for understanding weather and climate.

Stefan, a totally hip engineer who flew aboard each of these collection flights, has provided us with flight data he acquired on two such flights - one occurring May 4, 1994 and another on June 3, 1994. By analyzing these graphs, you will hopefully learn 1) what a typical KAO flight looks like (how long it is, how high it goes, etc.), 2) how pressure and temperature vary as you go up through the troposphere, and 3) how to read some fairly challenging graphs. Have fun, and don't forget to thank Stefan if you ever see him.

KAO Flight Profile

Analyze the graph titled KAO Flight Profile - 5/4/94. This graph records the elevation of the KAO at different times throughout its flight on May 4, 1994. Time is shown at the bottom as hh:mm:ss in Universal Time (UT) which is 7 hours ahead of Pacific Standard Time.

1. Based upon the graph, what altitude did the KAO begin at? __________

2. At what time did the KAO take-off? __________

3. What was the altitude the KAO climbed to before leveling off for the first time? __________

4. How many minutes did it take to reach this altitude after take-off? __________

5. What did the KAO do next? Describe the flight path taken after this first leveling off point.

6. What was the final cruising altitude of the aircraft (the highest altitude the plane reached)? _________

7. At what time did the KAO reach this final altitude? __________

8. How many hours was this after take-off? __________

9. At what time did the airplane start its descent? __________

10. When did the airplane land? __________

11. How many minutes did it take the plane to descend from its cruising altitude to the ground? __________

12. How does this compare with your answer for the initial ascent?

13. How long did the entire flight last? __________

14. Now compare this graph (KAO Flight Profile -5/4/95) with the same graph for the June 3, 1994, flight (KAO Flight Profile - 6/3/94). Answer the following questions.

15. Which flight lasted longer? __________

16. Which flight flew higher? __________

17. Give three similarities between the two flights?

18. Give three differences between the two flights?

KAO Ascent Profile

Analyze the graph titled KAO Ascent Profile - 5/4/94. This graph is similar to the last graph except that it only shows the takeoff and it includes pressure data both inside the cabin of the KAO (triangles) and outside the airplane (boxes). Note that elevation is on the left axis and pressure (in atmospheres) is on the right axis.

1. Look at what happens to the outside air pressure as the airplane goes up in altitude. Describe what happens to the outdoor air pressure as you go up through the atmosphere.

2. Now lets look at specific pressures at specific altitudes. What is the outside air pressure (in atmospheres) when the airplane is at sea level (0 ft)? __________

3. What is the cabin pressure (in atm) when the airplane is at sea level? __________

4. What is the outside air pressure (in atm) when the airplane is at 37000 feet? __________

5. What is the cabin pressure (in atm) when the airplane is at 37000 feet? __________

6. How does cabin pressure compare to outdoor pressure when the plane is on the ground? __________

7. How does cabin pressure compare to outdoor pressure when the plane is in the air? __________

8. Give at least one reason why it is important that the cabin pressure is higher than the outdoor pressure (that is, why is it important for the cabin to be pressurized)?

9. If a hole suddenly opened in the airplane, which direction would air flow? Explain you answer using the pressure values at 37000 feet.

KAO Descent Profile
Analyze the graph titled KAO Descent Profile - 5/4/94. .

1. Describe what happens to the outside air pressure at the KAO descends through the atmosphere.

2. Describe what happens to the cabin pressure as the KAO descends.

3. If you look at the slope of the diamonds (altitude) you will notice that the slope changes when the KAO reaches 8000 feet. Describe how it changes.

4. Imagine that you are a pilot and give one possible explanation of why the slope changes.

The Challenge: Making a Graph from a Graph

1. All three of the previous graphs have time plotted on the bottom. From these graphs, you can figure out where the KAO was at any time shown and what the pressures were at that time. We can also graph how air pressure changes with altitude (instead of time). First, use the KAO Ascent Graph - 5/4/94 and the KAO Descent Graph - 5/4/94 to determine what the outside pressure was at each of the following altitudes. Find the outside pressure that corresponds to the time that the KAO was at a given altitude.

   Altitude (ft)	Ascent Profile - Outside Pressure (atm)	Descent Profile - Outside Pressure (atm)
   0 ft
   5000 ft
   10000 ft
   15000 ft
   20000 ft
   25000 ft
   30000 ft
   35000 ft
   40000 ft

2. Now, using this data, make a graph with altitude (in feet) on the bottom and Outside Pressure (in atmospheres) on the side. Use a different symbol for the descent data than you use for the ascent data.

3. What is the relationship between pressure and altitude?

4. Why does this relationship exist? That is, why does pressure change with altitude?

5. Did the ascent data agree with the descent data? Give a possible explanation of why this is.

Conclusion and Extra Credit Congratulations!!! You have now completed analyzing some of Stefan's data. Hopefully you now know more about the KAO, about pressure, and about reading graphs. For extra credit, you can

• answer all of the previous questions using data from the 6/3/94 flight
• plot pressure data from the 6/3/94 flight on the altitude/pressure graph above
• compare the flight/pressure profiles between the two flights.