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NUMERICAL METHODS AND DATA ANALYSIS ENG60404 Question 1 An electric car is an automobile that is propelled by one or more electric motors, using energy stored in rechargeable batteries

Mechanical Engineering

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NUMERICAL METHODS AND DATA ANALYSIS ENG60404

Question 1

An electric car is an automobile that is propelled by one or more electric motors, using energy stored in rechargeable batteries. The first practical electric cars were produced in the 1880s. Electric cars were popular in the late 19th century and early 20th century, until advances in internal combustion engines, electric starters, and mass production of cheaper gasoline vehicles led to a decline in the use of electric drive vehicles. From 2008, a renaissance in electric vehicle manufacturing occurred due to advances in batteries, illnesses, and deaths due to air pollution and the desire to reduce greenhouse gas emissions.  Several national and local governments have established government incentives for plug-in electric vehicles, tax credits, subsidies, and other incentives to promote the introduction and adoption in the mass market of new electric vehicles, often depending on battery size, their electric range and purchase price. The current maximum tax credit allowed by the US Government is US$7,500 per car. Compared with internal combustion engine cars, electric cars are quieter, have no tailpipe emissions, and lower emissions in general. Four electric car models as shown in figures 1(a to d) below are tested to see the ranges that these cars can travel. They have the same battery capacity and the only difference between them will be the design, weight, and aerodynamics. Table 1 to 4 shows the ranges in kilometre for these cars. 

 

1. Using the most appropriate statistical analysis and appropriate significant level, calculate whether these cars are having similar performance in term of mileage travel.

(34 marks)

2. Calculate if there are difference or similar performances between the cars.
   8. marks)
3. Calculate which the most performing cars between them.
   8. marks)

 

 

                            Figure 1a. 2018 Nissan Leaf.    Figure 1b. BMW i3 AMS 12 2016

 

                            Figure 1c. 2018 Renault ZOE        Figure 1d. Tesla Model 3 2017

 

			Table 1. 2018 Nissan Leaf mileage (km)
575	542	530	539	570	580	575	590	589	555
			Table 2. 2018 Renault ZOE mileage (km)
565	593	590	579	610	600	601	602	601	559
			Table 3. BMW i3 AMS 12 2016
600	651	610	637	629	641	641	642	644	644
			Table 4. Tesla Model 3 2017
725	700	715	685	710	700	700	701	703	705

 

 

[Total= 50 marks]

 

 

 

 

 

 

 

 

 

Question 2.

1. The following equation models the height flew by a modified quadcopter with respect to time. Write a MATLAB script that apply bisection method to determine the height flew by the quadcopter over the interval from t = 1 to t = 2 when given y(1) = 1.5 and h = 0.25.

(17 marks)

 

 

2. The volume of liquid V in a hollow horizontal cylinder of radius r and length L is related to the depth of the liquid h by 

 

Determine the value of h given r = 550 cm, L = 6 m and V = 8 m³ using the false position method. Write a MATLAB script that asks the user to enter 2 initial values and the relative error threshold value. Then, the program will iterate until the relative error value reaches below the threshold requested by the user and the final estimated value of the depth of the liquid, h, will be displayed out.

(33 marks)

 

 

[Total Marks: 100 marks]