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Pressure Versus Force: Landing On Ice!

Overview
Rationale
Grade Level
Objectives
National
Standards

Before
Class
Preparation
Materials
Time


Teaching
Sequence
Engagement
Explanation
Elaboration
Exchange
Evaluation

Authors
Background
Resources
Student
Materials
Activity
Review


Overview
In this activity students experiment with the relationship between pressure, force, and area. They determine the force and pressure exerted by a LC-130 on the McMurdo ice runway. LC-130's commonly are used for cargo and personnel transport in Antarctica. This activity includes components of a classroom activity originally written by Carole Bennett and later modified by her for inclusion in the National Science & Technology Week 1998 resource guide "Polar Connections"


Arrival at Williams Field, McMurdo Station. Photograph by S. Shipp, Rice University.


Rationale
Designing an airstrip on land is challenging. Designing airstrip on ice adds a few wrinkles. And to further complicate the engineering, make that ice a floating ice shelf! Engineers working on the runways for the huge and heavy LC-130's landing near McMurdo had their work cut out for them! The engineers must know the pressure exerted by the LC-130's on the runway to know if the planes can land safely. A mistake can mean that the plane and cargo break through the ice and end up in the cold ocean below the ice shelf.

Grade Level/Discipline
High School, Physical Science, Physics, Chemistry
Introduction to the Gas Laws

Objectives
Students will:
  • explore the relationship between pressure, force, and area
  • strengthen estimation skills

    National Standards

    Teacher Preparation for Activity
    Before class, prepare one pan of sand for each group of 4 to 5 students. Pour fine sand into the pan so that each pan has 5 to 10 centimeters of sand in the bottom. Add enough water to dampen, but not soak the sand. There should be no standing water in the pan. The sand should be damp enough such that a finger can be poked into the sand and the hole remains intact when the finger is removed.

    Materials
    For the teacher:
  • A pair of high heel shoes or dress shoes with a distinct heel
  • A pair of flat walking shoes or tennis shoes

    For each group of 4 to 5 students:
  • dish pan or similar container
  • fine sand to fill the bottom 5-10 cm of the pan
  • water to dampen the sand
  • newspapers to place under the pan to restrict the mess
  • damp towel to wipe the shoes
  • images of LC-130's
  • pencils
  • paper
  • calculator

    Time Frame
    1 class period

    Teaching Sequence

    Engagement and Exploration (Student Inquiry Activity)
    Provide each student group with a pan of damp sand, newspapers, and a damp towel. Ask the students to level the sand and pat it down to make it firm.

    Tell the student groups that one group member in high heels or dress shoes will step on the sand. What will the imprint look like? The students will then re-level and re-pack the sand and a second student in tennis shoes will step on the sand. What will the imprint look like? How will the two imprints be different? Have each student group record their hypotheses and then perform the experiment. Remind the students to record the results of the experiment. Were the results different from the hypotheses?

    Explanation (Discussing)
    As a class, discuss the findings of the student groups. Which footprint was deeper, the shoe with the heel or the tennis shoe? Is there a consensus? Can the students explain the results?

    The students may say that the individual wearing the high heel weighed more than the student wearing the tennis shoe. How can this be tested so that weight is not a factor? The students may suggest that one person repeat the experiment with high heels or dress shoes and with flat heels. The facilitator can demonstrate this by repeating the experiment using different shoes. What are the results of this experiment? Why is there a difference? What is different about the two shoes? The students should realize that the dress shoe has less area than the tennis shoe. The weight of the teacher was distributed across that area.

    This relationship can be expressed as: Pressure = Force / Area.

    As a class, use the equation to determine the pressure exerted by an elephant versus a person. Which do the students think will exert more pressure? Which would the students want to have step on them?

    The elephant keeps at least 2 feet on the ground when it walks. If you estimate each foot to have 40 in2 area, it exerts 8000 lb./ 80 in2 or 10 psi.

    Humans will only have one foot on the ground while walking. Estimate that the area of the heel on a man's shoe is 10 in2. When he walks, a 200 lb. man exerts 20 psi because the weight is supported momentarily by the heel. A 100 lb. woman exerts many more psi when she wears heels. Depending on the area of the heel, she can exert as much as 1600 psi under a "stiletto heel" 1/4 inch on a side. This explains why people with wood floors don't want women walking on them in high heels.

    Elaboration (Polar Applications)
    At McMurdo Station, Antarctica, there are no paved runways, so planes land on the ice. How might the planes be modified to land on ice rather than pavement? Some of the students may suggest that the planes land on skis, rather than wheels. Ask them how this could make a difference? Which will produce the largest pressure - skis or wheels?

    Ask the students to make some estimates about the area of the skis and the wheels. How about the weight of the plane? Just based on the area, can the students make a prediction of the order of magnitude difference there may be (the area varies - the weight of the plane does not)?

    Have students work in groups to solve the following questions:
    What is the pressure under the skis when the plane lands? What is the pressure under the wheels? We consider only the force and pressure exerted when the plane rests on the ice, not the extra forces created while it lands.

    Average weight of a loaded LC -130: 155,000 lb.

    Area of wheels where they touch the ice:
    2 main wheels 23 inches x 25 inches each
    nose wheel 15 inches x 12 inches

    Area of skis:
    2 main skis and 1 nose ski (20 inches x 62 inches each)

    Which should be used to land on sea ice? Why?
    Solution:
    Average weight of a loaded LC -130:
    155,000 lb.

    Area of wheels where they touch the ice:
    2 main wheels 23x 25 + nose wheel 15x 12 = 1330 in2

    Area of skis:
    2 main skis and 1 nose ski ( 20 x 62 each) = 3720 in2

    Pressure under wheels
    155,000 / 1330 = 116.5 psi

    Pressure under skis
    155,000 / 3720 = 41.7 psi
    Exchange (Students Draw Conclusions)
    As the ice softens in summer, the ice is unable to withstand the pressure exerted by the wheels and the planes must be adapted to skis. What does this mean for the use of the equation: Pressure = Force/Area?

    The skis have a greater area than the tires. By using skis the pressure is less than half of the former pressure (if they do not reduce the load; in reality, the load of the LC-130's must be lessened by 8000 lb. for ski use, so the actual pressure is 147,000 lb. / 3720 in2 = 39.5 psi).

    Extensions
    This activity can be modified by having the students think what the pressure must be in the tires of the family car (at least 86.6 psi).

    Before the class begins the activity, ask the students to estimate the weight of the family car, the area of tire in contact with the ground, the pressure of each tire. Have the students note their estimates for later comparison.

    For homework, ask the students to:

    1. Determine the surface area where each wheel contacts the ground by placing string snugly around the wheel-ground interface.

    2. Determine the pressure in EACH tire using a tire gauge.
    Were the student estimates close to the actual values? Once the students have acquired the appropriate information, calculate the weight of the family car:
    3. Since P = F/A, multiply the area of each tire by its pressure to determine the force (weight) exerted by the car through that tire.

    4. Add all the forces (weights) and compare with the manual. It usually is pretty close.

    Evaluation (Assessing Student Performance)


    Authors
    Carole Bennett, Gaither High School, Tampa, Florida; TEA - 1996

    Background
    LC-130's are the four-engine turboprop transport aircraft used by the United States Antarctic Program for transport between New Zealand and McMurdo Station and between McMurdo Station and Amundsen-Scott South Pole Station.


    Boarding a LC-130 bound for Antarctica. Wearing the issued cold-weather gear is required; the flight will get chilly, and the clothing is an added safety precaution. Photograph by S. Shipp, Rice University.


    The LC-130's are C-130's that have been modified for polar use. They are equipped with skis and designed for landing on snow and ice. LC-130's can carry approximately 27,000 pounds of cargo and personnel (don't be fooled - personnel are considered cargo!). The planes carry enough fuel to travel from Christchurch, New Zealand to McMurdo Station - one way!

    LC-130's are capable of flying from McMurdo to the South Pole without refueling. Once at the South Pole, the engines are never shut down to prevent mechanical failures. Flights between McMurdo and South Pole are frequent from late October to mid-February; the station is isolated at all other times!


    Cargo strapped into the LC-130 for the trip to McMurdo Station includes Philip Bart and Mark Herring of Rice University, Jordan Franceschini and Martin Hilfinger of Hamilton College, and Kathy Licht and Jiang Xiao of the University of Colorado. Photograph by S. Shipp, Rice University.


    At McMurdo Station, the LC-130's land either on a sea-ice runway if the temperatures are sufficiently cold (from October into December), or on one of two strips, Williams Field or the Pegasus Runway. Williams Field ("Willie Field" to the locals) is used by ski-equipped planes. Landings are a little bumpy! Pegasus is a harder, smoother ice runway that is used by wheeled aircraft. In the summer, temperatures warm enough to make the Pegasus runway unusable.

    Resources
  • U. S. Navy, VXE-C Public Affairs Officer, Lt. Susan Merriman;
  • Coutrney W. Willis, Univ. of Northern Colorado, Greeley, CO
  • Dr. Mary Ann Davis, Tampa, Florida
  • The United States in Antarctica; Report of the U.S. Antarctic Program External Review Panel, 1997

    Student Reproducible Masters

    We look forward to hearing from you! Please review this activity.



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