Minimum Wing-Beat Frequency - Stress-Strain Graph - Engineering Assignment Help

Assignment Task :

QUESTION 1: Proportionality and Scaling  .

An empirical equation is obtained by doing a linear regression fit to a log-log  plot of observed wing-beat frequency (fw) compared to body mass (Mb) of many  species of bats. The data and corresponding relation are shown in the figure.

1(a). With reference to the above plot, explain what is meant by an allometric  scaling law.  

The largest existing bats (Pteropus) have a body mass of about 2 kg. Fossil  remains for an extinct bat species, Pteropus Gigantus, indicate that this bat  species had a body mass of about 3.5 kg, but was incapable of flight. 

Two scaling laws can be derived from physics concepts. 

1. The maximum wing-beat frequency (fw,max) which can be achieved within  metabolic rate constraints is proportional to Mb-1/3.  

2. The minimum wing-beat frequency (fw,min) which is required for flight is  proportional to Mb-1/6.  

1(b). Explain how these two scaling laws predict that there is a maximum  bat body mass above which bats would not be able to fly. 

QUESTION 2: Elasticity 

2(a). With the aid of a diagram, explain what a stress-strain graph is. 

Parkour (or its “acrobatic” version called  Freerunning ) has emerged as a non-combative form of military obstacle course training usually performed in urban landscapes. Many maneuvers involve landing on both feet  from heights which normally result in injury if not for the exceptional skill and technique of the participants. 

A person can break the long bones  of the leg by jumping from aheight  and landing on his or her feet on hard ground. The most vulnerable  weight bearing bone is the tibia, and  the compressive stress on this bone  will be greatest at the point where  the cross-sectional area is least. In  other words, just above the ankle. At this point, the tibia has a cross-sectional area of about 3 cm2. 

CT Scan showing the cross sectional area and geometry of the tibial compact bone. (Note.- crosssectional area corresponds to the cross sectional area ofthe roughly circular ring of compact bone and does not include the cross sectional area of the inner hole filled with marrow) 

2(b). What isthe maximum compressive force, Fmax, that both tibia (i.e. assume landing on both feet simultaneously so that the impact is distributed equally  over both legs) can withstand without compressive fracture? Hint. The  maximum compressive stress of compact bone is 1.7x108 N/m2as indicated in the  lecture notes. 

2(c). Use kinematic equations to show that the speed, v, acquired in a fall  through a height, H, starting from rest , is given by v2=2gH, where g = 9.8 m/s2. 

Poor Landing Technique: If a person lands flat on both feet stiffly, that is, without

bending the knees or having the heal slightly raised, the deceleration distance, D, is  approximately 1 cm (compression of the bones, joints, ground, etc).  

2(d). Determine the maximum jump height, Hmax,poor, without compressive  fracture of the tibial bones. Hint, Use kinematic equation and Newton’s 2nd Law  to first show that the average force required to decelerate the person is Fdecel =  mgH/D, where m is the mass of the person.

This Engineering Assignment has been solved by our Engineering Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.