1 )( )( )( TRANSPORTATION. Energy Cost of Transport. Problem Set Solutions

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1 TRANSPORTATION Energy Cot of Tranport Problem Set Solution For the following problem, we have provie all of the value neee to olve them. However, thee number are relatively eay to etimate or fin online an we recommene you encourage your tuent to look up the number themelve. You can even take out our number an give each tuent a ifferent vehicle to look up (i.e. for Problem, give each tuent a ifferent cruie hip to calculate the energy cot of). Problem : Cruie Ship What i the energy cot of tranport of a cruie hip? I there any ifference between the worl larget paenger veel (Royal Caribbean Oai of the Sea), a more tanar cruie hip (i.e. Celebrity Summit) an the now retire Queen Elizabeth II? The Oai of the Sea ha an output power of 60 MW, a ervice pee of 0. knot, an a paenger capacity of 5,400 people. The Celebrity ummit ha an output power of 50 MW, a ervice pee of 4 knot, an a paenger capacity of,450 people. Aume the mechanical efficiency of thee hip propulion ytem to be 5% (40% for the ieel engine, 70% for the propeller, an 90 ome % for the tranmiion). The Queen Elizabeth II ue 433 tonne of fuel each ay, travel 5500 km in 6 ay, an ha a paenger capacity of,790. Problem Solution: Cruie Ship Specification of the Oai of the Sea: P output = 60 MW ε = 0.5 Service Spee = 0. kt = 0.4 m/ Paenger Capacity = 5,400 Energy Cot of 60 MJ Tranport ( 0.4 m 000 m ) 440 MJ/km/00 people km 5400 people Specification of the Celebrity Summit: P output = 50 MW Service Spee = 4 kt =.3 m/ Paenger Capacity =,450 Energy Cot of 50 MJ Tranport (.3 m 000 m ) 680 MJ/km/00 people km,450 people Specification of the Queen Elizabeth II: Fuel Uage = 433 tonne/ay

2 Duration of trip = 6 ay Diplacement = 5500 km Paenger Capacity =, ,000 kg 4 MJ Energy Cot of Tranport ( 6 ay ay L 00 MJ/km/00 people L kg 5500 km,790 people The energy cot of tranport of cruie hip varie ubtantially epening on the veel (ranging from MJ/km/00 people). Problem : Skytrain Etimate the energy cot of tranport of the Skytrain in Vancouver. We know that the top pee i 60 km/h, it accelerate once between each tation, the capacity i 300, the ma of the empty Skytrain i 76,000 kg, the cro ectional area i m an the enity of air i.9 kg/m 3. We have choen to calculate the energy cot between tation that are km apart, an have etimate the itance of acceleration an eceleration to be 300 m each, the coefficient of rolling reitance to be 0.00, the rag coefficient to be 0.5 an the mechanical efficiency of the motor to be 80%. Problem Solution: Skytrain Spee = 60 km/h Ditance between tation = km acceleration per tation capacity = 300 m = 76,000 kg(train) + 300*80kg (people)= 00,000 kg A = 3 m x 3.6 m = m ρ air =.9 kg/m 3 Etimation: acceleration / eceleration = 300 m μ = 0.00 C D = 0.5 Efficiency of electric motor = 80% ) The total energy for each km i ue to acceleration an overcoming air rag an rolling friction (the rag will be neglecte uring the acceleration phae). Energy for acceleration:

3 W acceleration mv (00,000 kg6.7 m/) 4 MJ Energy for maintaining pee: W W W (0.0000,000 kg9.8m/.7 MJ.3 MJ 3 MJ rag mg C D Av 700 m) (0.5m No work i one uring the 300 m where the Skytrain i ecelerating..9 kg/m 3 6.7m/) If the motor are 80% efficient, the total energy require i 7/80% = MJ when traveling km. Energy Cot of MJ Tranport ( ) 3.5 MJ/km/00 people km 300 people (400 m) Problem 3: TGV v. Shinkanen How oe the energy cot of tranport of the TGV (France High Spee Rail) compare to that of the Shinkanen (Japan High Spee Rail) when they are both travelling at full pee? The TGV ha a maximum velocity of 30 km/h, a maximum capacity of 36 people, a ma of 45,000 kg when full an a power output of 9.8 MW. The Shinkanen ha a maximum velocity of 70 km/h, a maximum capacity of,33 people, an a power output of 3. MW. Problem 3 Solution: TGV v. Shinkanen TGV: V max = 30 km/h Capacity = 36 people m full = 45,000 kg P = 9.8 MW ε = 0.8

4 Energy Cot of 9.80 MJ Tranport ( Shinkanen: V max = 70 km/h Capacity =,33 people P = 3. MW ε = 0.8 Energy Cot of 3. MJ Tranport ( h 30 km h 70 km 3600 ) 36 MJ/km/00 people h 36people 3600 ) 6 MJ/km/00 people h,33 people The energy cot of tranport for Japan Shinkanen i half of that of France TGV. Problem 4: Rubber Tire Metro What i the energy cot of tranport for the MP 89 ue on the Pari Metro? The maximum velocity i 80 km/h, the maximum capacity i 70 people, an the power output i.8 MW. Problem 4: Rubber Tire Metro V max = 80 km/h Capacity = 70 people P =.8 MW ε = 0.8 Energy Cot of.8 MJ Tranport ( 0.8 h 80km 3600 ) 3 MJ/km/00people h 70people Problem 5: Lower Limit of Tranportation What i the lower limit of tranportation cot for tranporting 0 tonne, 0 km uing a barge or teel wheel on teel rail? Problem 5 Solution: Lower Limit of Tranportation Cot Steel on teel: If it travel lowly, we can ignore air reitance an rolling reitance i the only thing we have to take into account. m = 0,000 kg = 0,000 m

5 μ = W mg (0.0000,000 kg9.8 m/ 96,000 J 0. MJ 0,000m) So the lower limit of tranportation cot i 0. MJ/0 tonne/0 km when uing teel on teel. Barge Tranport: There i actually no lower limit to the energy cot of barge tranport ince in thi ituation, the rag of the water i the only thing we have to take into account an rag goe to zero a velocity goe to zero. Thi i the ame for maglev train, airhip an anything ele that oe not have oli contact with the groun (not airplane). If we were to ue a barge at a very low pee, knot or m/, what woul be the tranportation cot? We can etermine the type of flow, whether turbulent or laminar, by calculating the Reynol number, Re. ul ul Re enity of water 05.9 kg/m u pee of the barge m/ L length of the bargee 0 m flui ynamic vicoity.00x0 flui kinematic vicoity.838x0 C rag coefficent.838x N/m 6 m / (ue in the calculation of F ul (m / ) *(0m) Re.8838x0 m / If Re 000, it inicate laminar Flow If Re rag 6 5.3x , it inicate turbulent flow.in thi cae, the flow i turbulent, an rag force, ) F rag,i calculatea F W rag v C F rag A v C A 3 (05.9 kg/m m/) 0.476MJ (C 30 m ) (0,000 m)

6 In the particular cae we have calculate ( m/), the tranport cot of the barge i more than the teel wheel/teel rail lower limit. Ship Technology. Oai of the Sea Luxury Cruie Liner (online) technology.com/project/oaioftheea/pec.html [4 Aug 00]. Wikipeia. Celebrity Summit (online). [4 Aug 00]. Wikipeia. Canaa Line (online). [4 Aug 00]. Hyunai Rotem. Canaa Vancouver LRV (online). [4 Aug 00]. Wikipeia. TGV (online). [4 Aug 00]. Wikipeia. 700 Serie Shinkanen (online). [4 Aug 00]. Wikipeia. MP 89 (online). [4 Aug 00]. Wikipeia. Rolling Reitance (online). [ Aug 00]. Cyberia, Hyroynamic Drag of mall ea Kayak (online). [ Sept 00]. Brittany Tymo 00 08