climate-scenario-1

[djinnome]

Scenario 1: Connecting Climate with Aircraft Performance

Over the years we’ve seen increases in surface temperatures and atmospheric temperatures, driven by climate change. We are interested in understanding how increasing atmospheric temperature directly affects the domain of aircraft performance via physical laws.

Let’s begin by plotting historical and forecasted temperature for select locations - Guam and Little Rock, Arkansas.

1. Search for historical data and climate model output (for future projections) for monthly mean of the daily maximum temperature. For climate model data, search for CMIP5 or CMIP6 outputs.

2. For each of the two locations (Guam, and Little Rock), plot monthly mean of the daily maximum temperature (daily Tmax) for Jan – Dec for the following:

   • With historical observed data of Tmax, 1970 – 1999
   • Climate model output for Tmax, 1970—1999 (how well does model output reproduce the observed data?)
   • Climate model output for Tmax, 2020—2049 (future forecast)
   • Climate model output for Tmax, 2040—2069 (future forecast)
   • Climate model output for Tmax, 2060—2099 (future forecast)

3. The US Andersen Air Force Base (https://www.andersen.af.mil/) is located in Guam. For the rest of the questions in this scenario, we are interested in a spatial scale relevant to the size of the base – 50 km. If needed, run downscaling algorithms on the climate data found in Q1, to match this spatial scale.

4. This question asks you to explore how aircraft takeoff distance may be affected by increasing temperatures (as forecasted by climate models). To calculate takeoff distance, you will have to take the temperature data from Q1-3 climate model outputs, and transform it according to Figure 1, and the following equations

Figure 1. Calculate aircraft takeoff distance, from climate model outputs

[djinnome]

Ideal Gas Law

• Classically Expressed: $PV = nRT$
• Expressed with Density: $PM = \rho RT$

Where:

• $P$: pressure (Pa)
• $V$: volume ($m^3$)
• $n$: number of moles of gas (can be considered “mass”)
• $R$: gas constant
• $T$: temperature (K)
• $M$: molar mass (g/moles)
• $\rho$: density (g/$m^3$)

Note: $\rho \propto \frac{1}{T}$ (density is inversely proportional to temperature)

Simplified Equation for Takeoff Distance

A simplified equation for takeoff distance is given as:

$$D = \frac{T_{to}^2}{2\mu(W/S)(\rho V_s^2)}$$

Where:

• $D$: Takeoff distance (m)
• $T_{to}$: Takeoff thrust (N)
• $\mu$: coefficient of friction between tires and runway (0.03 for dry asphalt)
• $W$: weight of the aircraft (N)
• $S$: wing reference area ($m^2$)
• $\rho$: air density (kg/$m^3$)
  • Air density is related to air temperature (i.e., Ideal Gas Law)
• $V_s$: stall speed (m/s)

Task

To understand what happens to aircraft performance as the temperature changes, please fill out the following table for the different plane types, carrying two different loads, for the years 2050, 2075, and 2099. Search the literature to find wing reference area, max load, stall speed, and take-off thrust. Please show values used.

Table 1. Takeoff distances for aircraft carrying max loads, at Guam

Aircraft	Year	Takeoff distance based on monthly mean of daily Tmax	Takeoff distance based on monthly mean of daily Tmin
Boeing 747-8F	2050
	2075
	2099
Lockheed C-130J	2050
	2075
	2099

Table 2. Takeoff distances for aircraft carrying max loads, at Little Rock Table 2. Takeoff distances for aircraft carrying max loads, at Little Rock

Aircraft	Year	Takeoff distance based on monthly mean of daily Tmax	Takeoff distance based on monthly mean of daily Tmin
Boeing 747-8F	2050
	2075
	2099
Lockheed C-130J	2050
	2075
	2099

Table 3. Takeoff distances for aircraft carrying 80% of their max loads, at Guam

Aircraft	Year	Takeoff distance based on monthly mean of daily Tmax	Takeoff distance based on monthly mean of daily Tmin
Boeing 747-8F	2050
	2075
	2099
Lockheed C-130J	2050
	2075
	2099

Table 4. Takeoff distances for aircraft carrying 80% of their max loads, at Little Rock

Aircraft	Year	Takeoff distance based on monthly mean of daily Tmax	Takeoff distance based on monthly mean of daily Tmin
Boeing 747-8F	2050
	2075
	2099
Lockheed C-130J	2050
	2075
	2099

[djinnome]

Here is some optional background reading on aircraft takeoff and landing analysis

• https://society-of-flight-test-engineers.github.io/handbook-2013/fixed-wing-performance-standardization.html
• https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/takeoff-landing-performance/
• https://www.t-craft.org/documents/reference/DA_Safety.pdf