Standard Atmosphere final
pdf
keyboard_arrow_up
School
Georgia Institute Of Technology *
*We aren’t endorsed by this school
Course
1601
Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
Pages
9
Uploaded by GeneralBoarMaster702
1 AE 1601 –
Standard Atmosphere Activity Turn in on Canvas (Individual) Background Information Andrea Romero AE 1601 The purpose of this exercise is to gain an understanding of planetary atmospheres by comparing the atmospheres of Venus and Mars to the Earth standard atmosphere. Atmosphere profiles for Venus and Mars will be constructed based upon published data obtained by space flight entry probe observations. There are several handy equations and constants used in this exercise. They are listed below. a.
Relation between geometric altitude (
h
G
), geopotential altitude (
h
), and planet radius (
r
P
) 𝑟
𝑃
ℎ
= ℎ
𝐺
𝑟
𝑃
+ ℎ
𝐺
b.
Hydrostatic Equation for Isothermal Layer 𝑝
2 = 𝑝
1
𝑒
−
[
𝑔
0
/(
𝑅𝑇)](ℎ
2
−ℎ
1
) c.
Hydrostatic Equation for Gradient Layer 𝑇
2
−𝑔
0
/(
𝑎𝑅
) 𝑝
2 = 𝑝
1 (
𝑇
)
Note: a is the temperature lapse rate with altitude. d.
Equation of State (Ideal Gas Law) 𝑝
= 𝜌𝑅𝑇
e.
Specific Gas Constants (R): Earth = 287 J/(kg K), Mars = 188.92 J/(kg K), Venus = 188.92 J/(kg K) f.
Planet Radii: Earth = 6,378.14 km, Mars = 3,397.2 km, Venus = 6,051.8 km g.
Gravitational Acceleration at Planet Surface: Earth = 9.8 m/s
2
, Mars = 3.8 m/s
2
, Venus = 8.9 m/s
2
0.
Look up and include the GT honor code statement! 1.
Using the online Georgia Tech Library website (library.gatech.edu), access the “Full
Text Online”
of the following journal article: Seiff, A., “Atmospheres
of Earth, Mars, and Venus, as Defined by Entry Probe Experiments,”
J
Type equation here.
urnal of Spacecraft and Rockets, Vol. 28, No. 3, May-June 1991, pp. 265-275.
𝑝
= 𝑝
(
𝑇
) What is the Digital Object Identifier (doi) number for this article? It is DOI number 10.2514/3.26240 2.
The standard atmosphere for the Earth is modeled as a series of gradient and isothermal regions, as shown in the figure from Anderson’s book (Introduction to Flight). Note that this figure uses
geopotential altitude. Calculate the pressure in the standard atmosphere at 10,000 feet geopotential altitude. You will have to look up the values of the necessary constants in the English unit system. Show your work, and state which hydrostatic equations you use (isothermal/gradient). Watch your units! Intial info used: 10000 ft g=32.2 ft/s^2 R = 1717 ft lb/ (slug*degR) 𝑇
1
=518.7 degR p
1
=2.1162 lb/ft^2 Calculated Slope =a = ∆𝑇
/
∆
h = (390.5 degR-518.7 degR)/(36000 ft-0 ft)=-0.00356 degR/ft Gradient Temperature T(h)=
𝑇
1
+ a(
ℎ
2
−
ℎ
1
)
, then T(10000)=483.1 degR Gradient Pressure 𝑇
2
1
1
−𝑔
𝑇
/(
𝛼∗𝑅
)
P=(2.1162 lb/ft^2*(483.1 degR)/(518.7 degR))^-((32.2 ft/s^2)/(
-0.00356 degR/ft*
(1717 ft lb/ (slug*degR)))
3.
The figure below shows the measured temperature profiles for the Mars atmosphere recorded by the Viking landers. A linear fit (shown in red) has been made to the Viking Lander 1 data, with a single gradient layer from 0 to 40 km, and a single isothermal layer from 40 to 80 km. Note that the altitudes (z) are geometric altitudes. Fill in the missing values from the table. NOTE: You may use Excel for these calculations, but you need to state which equations and which inputs you used to calculate each column. You will need to copy your results onto this worksheet, but please turn in your Excel sheet with your submission
h
G (ft) h (ft) T (R) p (lb/ft^2) (slugs/ft
3
) 0 0 230 7.57E+02 1.7E-05 65616.8 65232.76161 -208.9506324 2.316373405 6.00E-06 131233.6 129706.3848 -824.651752 0.223693921 7.33E-07 196850.4 193434.0446 -1433.229175 0.016536681 5.42E-08 262467.2 256428.6126 -2034.805822 0.001259666 4.13E-09
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
𝑝
= 𝑝
(
𝑇
) Imperial MARS SI Mars Standard Atmosphere Table: h
G (km) h (km) T (K) p (N/m
2
) (kg/m
3
) 0 0 230 7.50E+02 1.73E-02 20 19.882945 189.76589 110.908369 3.09E-03 40 39.534505 150 10.7105045 3.78E-04 60 58.958695 150 0.79177924 2.79E-05 80 78.159439 150 0.06031303 2.13E-06 er gas constant J/kg K 188.92 formulas used h=rp/(rp+hg)hg density=p/(RT) from 0 -20 m T=T1+a(h-h1) 𝑇
2
1
1
−𝑔
𝑇
/(
𝛼∗𝑅
)
From 20m+ T is a constant and P=p1+e^((g/RT)(h/h1)
data radius ® units km val planet 3397.2 mars for h I used a formula to get t I first need alpha alpha k/km -2.023549 neg means its getting cold
gravity m/s^2 3.8
4.
The figure below, taken from the Seiff paper, shows the measured temperature profiles for the Venus atmosphere recorded Pioneer Venus probes. A single linear gradient layer (shown in red) provides a very good fit to the measured data. Again, the Seiff altitudes are geometric altitudes. Fill in the missing values in the table below (next page). NOTE: You may use Excel for these calculations, but you need to state which equations and which inputs you used to calculate each column. You will need to copy your results onto this worksheet, but please turn in your Excel sheet with your submission. h
G (ft) h (ft) T (R) p (lb/ft^2) (slugs/ft
3
) 0 0 1323 1.98E+05 1.33E-01 65616.8 5540.777275 2381.4 4.22E+04 4.20E-02 131233.6 5785.025214 459 3.20E+03 6.16E-03 196850.4 5871.29785 459 3.20E+03 6.16E-03
𝑝
= 𝑝
(
𝑇
) formulas used h=rp/(rp+hg)hg density=p/(RT) T=T1+a(h-h1) 𝑇
2
1
1
−𝑔
𝑇
/(
𝛼∗
R)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Venus Standard Atmosphere Table: VENUS SI h
G (km) h (km) T (K) p (N/m
2
) (kg/m
3
) 0 0 735 9.50E+06 6.84E+01 20 19.9341217 494.20946 2020450.09 2.16E+01 40 39.7373519 255 152998.945 3.18E+00 60 59.4109755 255 152998.945 3.18E+00 data units val planet radius ® km 6051.8 VENUS alpha k/km -12.079315 gravity m/s^2 8.9 gas constant J/kg K 188.92 5.
Use the 1976 Standard Atmosphere Tables (can be found on Canvas and online) to fill in the table below for Earth. You don’t need to do calculations for this part. Discuss briefly how the atmosphere of earth
compares to that of Mars and Venus, in terms of temperature, pressure, and density. imperial h
G (ft) h (ft) T (R) p (lb/ft^2) (slugs/ft
3
) 0 0 518.688 2.12E+03 2.38E-03 65616.8 5813.090986 389.988 1.15E+02 1.73E-04 131233.6 6082.520819 469.638 6.26E+00 7.77E-06 195210 6176.339091 460.602 5.72E-02 7.24E-07 Earth Standard Atmosphere Table: EARTH SI h
G (km) h (km) T (K) p (N/m
2
) (kg/m
3
) 0 0 288.16 1.01E+05 1.23E+00 20 19.9374818 216.66 5.53E+03 8.89E-02 40 39.7507066 260.91 3.00E+02 4.00E-03 59.5 58.9500702 255.89 2.7403 3.73E-04 data units val planet radius ® km 6378.14 EARTH alpha k/km -0.8118094 gravity m/s^2 9.8 gas J/kg K 287
constant All of the three planets
’
pressures decrease as altitude decreases, which also happens with density. With density the order is Venus has a larger one that Earth and Earth a larger one than Venus. I found interesting, thought, that Mars basically has 0 atmosphere until 60 km from its surface/ Earth has very obviously a more stable temperature than either Venus or Mars, even when considering the increase in temperature that Earth has form km 20 to 40 from its surface. For all the calculations of VENUS and Mars I used the formulas in the first sheet of this WORD document the way we set them up in class. At first it was somewhat difficult to really understand the relation between the variables and the value we wanted for each column btu reading about it helped so that they would not just be numbers summed up or multiplied by others. For the English units (imperial units) of all the data I looked for the factor that made them equal and multiplied the respective quantities but I also checked that it had the same results if I had just changed the variables in the equation and not the specific piece of information’s value
only
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help