Paul Laurence Dunbar High School results:
Flying on Mars & Testing on Earth

If you were going to design an aircraft to fly exploration missions on Mars (or other planets), how would you start?
Students: Han and Michael

Answer (1)
First of all, the engineers need to analyze the environment they are around, so as a result the mass densities of all of the gases in the air need to be quantified to make the metal platings or other materials on the aircraft stable and sturdy. For example, high oxygen levels may rust and damage the coverings of the base and outer protection. Because Mars has a 95.3% carbon dioxide content, and with the low temperatures, another important factor is the formation of ice crystals and freezing on the hull of the spacecraft because many parts of Mars are so cold, but the atmosphere also allows for gradual warming so there are minimal and maximal levels for temperatures.

Then we need to examine barometric pressures so that the cabin pressure can equalize for the pilots and so the craft does not suffer structural damage from the extremely high or low partial pressures that exist.

To compensate for these opposing variables, scientists and design engineers are required to modify the exterior and interior modules of the final spacecraft to fit the right conditions. For example, there is expected to be some turbulence in the Martian skies and the wings of the plane need to be heavy to the point where it is not flimsy but light to the point where it doesn’t entirely snap in half from the weight. That brings us to our next point, gravity. Due to the lower gravity numbers, materials and atomic elements may behave in a unique way physically on the fourth planet.

http://www.ucls.uchicago.edu/MartianSunTimes/
?/docs/mars_stats.html

You might begin by looking at important properties of the planetary atmosphere and how they relate to flight. Planetary atmospheres, including that on Earth, are made up of various gasses. On Earth, the main constituents are Nitrogen and Oxygen; on Mars it is Carbon Dioxide. The study of the motions of gasses and liquids is called fluid dynamics. Whether you are considering the wind and its part in weather or the flow over a wing, fluid motion is an important subject.

Make a list of all of the variable quantities that appear in the dimensionless Reynolds and Mach Numbers. Define each quantity. List appropriate units for each quantity in both English and Metric units. Show that the Reynolds Number and Mach Number are dimensionless. Write down two sets of quantities (density, velocity, length, and viscosity) with air as the fluid that result in the same Reynolds Number. What if one set included properties of a gas (air, for example) and the other included properties of a liquid (water). Can you write down two sets (density, velocity, length and viscosity) so that the Reynolds Number is the same?
Students: Connie and Mimi

In the study of fluids and forces, two important dimensionless quantities that are used to describe flight and aircraft are the Reynolds Number and Mach Number.

The Reynolds Number, Re, is the ratio of inertial forces to viscous forces where ρ is the fluid mass density, v is the fluid velocity, L is a characteristic length such as wing width (chord), and μ is the fluid viscosity.

The Reynolds Number is used to predict the occurrence of different flow characteristics such as laminar, transitional, or turbulent flow, as well as to define experiments with dynamic similarity so that smaller scale models can be tested in wind tunnels or water tunnels during the design process instead of building and testing more expensive full-scale models.

The Mach Number, M, is the ratio of the speed of an object in a fluid to the speed of sound in that fluid. where v is the speed of the object and vs is the speed of sound in the fluid. High-speed flight is categorized using the Mach Number.

Reynolds Number:

ρ = kg/m3 = lb/ft3

v = m/s =ft/s

L = m=ft

μ = kg·m−1·s−1= lb/(ft*s)

Re = kg/m3*m/s*m / (kg·m−1·s−1) --> dimensionless

Mach Number:

v = m/s = ft/s

vs = m/s = ft/s

M= (m/s)/(m/s) -->dimensionless

2 sets of quantities resulting in same Reynolds number:

1) ρ = 1.2 kg/m^3

μ = 1.72*10^-5 kg m/s

v = 2 m/s

L = 3 m

2) ρ = 1.2 kg/m^3

μ = 1.72*10^-5 kg m/s

v = 1.5 m/s

L = 4 m

WATER: ρ = 997.0479 kg/m^3

μ = 8.91*10^-4 kg m/s

v = 2 m/s

L = 5 m

Flow characteristics can be predicted by considering the Reynolds Number. Laminar flow is smooth, with the fluid particles following parallel paths as they move. For example, if a faucet is lightly turned on, the water is clear and forms a column with straight sides. Turbulent flow is not smooth, with the fluid particles following very different paths as they mix with each other. If the faucet is turned on more strongly, the water changes its appearance. Tubing on a stream flowing smoothly is a very different experience than white-water rafting. Laminar flow over an airfoil (the cross section shape of a wing) is also very different than turbulent flow. Transitional flow, like the name implies, is somewhere in between. For airfoils (note: pipe flow and other flows will be different), find Reynolds Number ranges for laminar, transitional and turbulent flow. Note that these will vary for different situations and applications, so different sources may give different ranges.
Students: Dustin and Rahuel

• laminar if Re < 2300
• transient if 2300 < Re < 4000
• turbulent if 4000 < Re

The Mach Number is used to categorize different flight regimes (for example, hypersonic). Find and list Mach Number definitions for different flight regimes. From these important dimensionless quantities, we can start a list of important atmospheric fluid properties including mass density, viscosity and the speed of sound in the fluid. Other important properties include temperature, pressure, and the chemical composition of the fluid.
Students: Eliott and Ben

·  Subsonic: Ma < 1
·  Sonic: Ma=1
·  Transonic: 0.75 < Ma < 1.2
·  Supersonic: Ma > all airflow above mach 1. Plane must be above mach 1.2
·  Hypersonic: Ma > 5

Think about everything that you know that flies, from creatures to toys to man-made aircraft and spacecraft. Make a list of all of the atmospheric fluid properties and characteristics that you can think of that might be important for flight.

What about sunshine (radiation from the sun)? Should this be on your list? Why or why not?
by Kevin and Kyle

·  Viscosity
·  Heat Capacity
·  Pressure
·  Mass
·  Speed of Sound in the Medium
·  Density
· Composition
·  Turbulence
· Temperature
· Compressibility
·  Sunshine is not an inherent quality of atmosphere. However, it does influence temperature and viscosity of the atmosphere. Sunshine and its ability to vary at different times should be noted when considering flight.

Re: the variation of temperature versus altitude
Student: Scott

Re: the variation of pressure versus altitude
Student: Shelly

On EARTH, pressure and altitude are inversely correlated, and the relationship is linear. Therefore, when altitude increases the pressure decreases. The relationship is similar on MARS, where pressure and altitude are also inversely correlated.

Re: the variation of density versus altitude
Students: Han and Michael

In addition to knowing characteristics of the Martian atmosphere, to build and test a Mars Airplane on Earth, we also need to know the same characteristics of Earth’s atmosphere.

At what altitude on Earth is the density the same as that at low altitudes on Mars?
Students: Dustin and Rahuel

40 km; they are both equal at approximately 10^-5 g/cm^3

At what altitude on Earth would you propose to conduct a flight test to approximate the conditions for low altitude on Mars?
Students: Elliott and Ben

Flight conditions will be similar when the laminar flow is the same. Since laminar flow depends on Reynold's number, which depends on density, similar flight conditions occur when air density is the same. According to question 11, the atmospheric density at an altitude of 40km on earth is approximately the same as atmospheric density at low altitudes on mars. So, the test flight should be conducted at around 40km above earth.