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- The study of size and its consequences.
- Physical laws (physics) provide size constraints on living body forms, organs and functions.
- Organsimal size range is great, not all "designs" work equally well for all sizes of organisms.
- Physical characteristics often produce different actions, and are dependant upon Laws of Physics.
- Different sizes resonate at different frequencies; hence different tones for these instruments.
- Tonal relationship to frequency=absolute.
- Physical limitations require proportion changes in different sized objects.
- Relatively larger object encloses a greater volume.
- Increased volume means dimmer interior, so window area must be increased to allow more light to enter.
Elephant vs. bug
- Columnar limbs support great weight - gravity is a serious concern for large animals.
- Surface tension matters to a small organism.
- Length, area and volume relationships - constant shape but change in body size increases surface area some but causes and even greater relative increase in internal volume.
- Surface area is squared
- Volume is cubed
Surface area and volume relationships
- Physiological performance depends on surface area and volume relationships.
- Therefore, larger animals must have different proportions than smaller ones.
- Volume increases cause increased mass.
- Body support by limbs with strength according to x-sectional area (x2)
- Mass increases according to (x3)
- I.e., shape changes as an organism grows to maintain proper relationship among functional regions.
- Physiological processes scale with body size, as do anatomical features. O2 consumption decreases per unit of mass as size increases. This is why larger organisms have lower metabolic rates than do small animals.
- Animal morphology must be alterable to accommodate changing mass and length of areas.
- Animals have different sizes at different ages.
- As body mass increases, bone attachment surfaces and other surface features become relatively larger. This exaggeration relates to x-sectional area of the attachment surface and the cubed mass of the increasing volume of muscles, etc. attaching to the bone.
- change in shape that correlates with size.
- Phylogeny may be related to allometry if phylogenetic tend includes a relative change in size and proportion through time.
- Allometry can be positive, negative or neutral=isometry.
Allometric trents in phylogeny
- Shape change accompanied by change in size.
- Horn length in titanotheres, increase is allometric.
growth occurs so that region relationships remain the same; body proportions remain constant.
D'Arcy Thompson Transformation Grids
These show where and by how much a region of a structure changes with respect to a different growth stage, between taxa, or to demonstrate phylogenetic changes through time.
use to understand phylogenetic changes. One taxon is reference, points on it are shown in relatively the same place as deformations of the shape in comparison taxa to show shape changes of regions of descendant taxa. This can show patterns of shape change and trends through time.
Pros and Cons of large size
- pros: Larger animals have fewer predators, longer lives, longer juvenile periods for learning.
- cons: Require more food, larger territories, longer gestation times, produce fewer offspring, and recover more slowly from population losses.
- in larger forms: Body form must be altered to support more weight=graviportal adaptations.
Refinements to transformational analyses
- Thin plate spline analysis
- Landmark analysis
- 3D imaging methods, ie, why scans and computer reconstruction of structures can provide so much information.
- However, all methods are a means of determining the changes in shape of an organism in relation to changes in size.
A constant is added to the structure length during each time interval.
- length multiplied by a constant in each time interval.
- Larger lobster claw is a weapon; it grows geometrically as body size increases:
- The growth pattern of a feature may permit behavior changes.
- Small lobsters cannot use a claw larger enough to be a sufficient weapon, although once it is larger they can.
- Small lobsters have to hide from potential danger.
- Larger lobsters armed with a very large, strong claw can defend themselves without running away if necessary.
- Analysis of biological "design"
- Components include: length, time, force and mass
a property of matter
- a property of force.
- When weight does not affect an object it is still difficult to move under water or in space because of mass.
rate of changes of an object's position
rate of change of velocity
force divided by area.
- the rate at which work is done.
- Power not appropriate to use in discussing biomechanical "work" because as it is used in physics, it always indicates that work is done.
- In biological systems, effort may be exerted, but if nothing changes nothing is accomplished; therefore no work is done, so no power has been generated.
Center of mass
- mass of animal as if it is concentrated at a single point.
- Center of mass may not always be within the body of the animal.
Center of gravity
animal's body evenly balanced around this point.
Cartesian coordinate system
- graphically shows position of an object in three-dimensional space.
- Gives a unique location of the object and a precise means of describing that location.
- describe measurements with a magnitude and direction.
- Represented by a Cartesian reference system.
- Forces can be calculated, was with a bear dragging a seal.
- Combination of vertical + horizontal.
- Knowing angle theta with surface and F allows calculation of component forces graphically or trigonometrically.
First law of Inertia
Everybody continues in a state of rest or in a uniform path of motion until acted upon by a new force.
Tendency of a body to resist change in its state of motion.
Second Law of Motion
- Change in an object's motion is proportional to the force acting on it.
Third Law of action, reaction
Between two objects in contact, there is an equal and opposite reaction for each.
Einstein's Theory of Relativity
Placed limits on Newtonian laws, but they work well enough until we get close to the speed of light, so will be used here.
Free body diagram
depicts an isolated body part with forces acting on it.
- A rigid bar that can be pushed or pulled to rotate about a fixed point.
- Levers re moved by muscles that attach at various points along them.
- the amount of force generated or required is determined by:
- Position of load relative to pivot.
- Point of attachment of muscles.
- Fulcrum, pivot (point) or axis of rotation.
- Pivot points are usually at joints.
- A force which acts at a distance from the fulcrum and turns the lever.
- Forces generated by levers producing work are in-torques (=in-forces) and out-torques (out-forces).
- If more force is required, the "out" is shortened and the "in" is lengthened - increases force at the expense of speed.
- If more speed is required, the "in" is shortened and the "out" is lengthened - increases speed at the expense of force.
Type I levers
- Forearm of a digger that emphasizes force at the expense of speed of movement.
- Forearm of a runner that sacrifices force for speed.
- You cannot have both at the same time.
Class III lever
Also an action at the elbow, but flexion, using the biceps.
The ratio of Fo/Fi, the output force to the input force.
The ratio of the output lever to the input lever arm.
Muscle gear ratios
Animals have limbs with muscles of different mechanical advantages that allow different contributions of force or speed.
- exerts force on all objects on land.
- The larger the object the more importance of the force of gravity.
dense, incompressible fluid
Fluid media resisting passage of objection
(=skin drag) occurs from pressure on skin of animal as it passes through the medium.
general layered patterns of fluid flow.
fluid layer that adheres to the surface
boundary layer separation (=flow separation) because stremlines cannot close smoothly behind object, fluid behind object moves faster, pressure decreases.
- combination of friction (skin drag) and pressure drag.
- Related to the shape of an object as it forces itself through the fluid.
- Smooth shape passes more easily.
- Tapered shape passes more easily.
- Narrow, or sharp edges pass more easily than broad or thick edges.
- Explains wing shape among different organisms and aircraft.
- The volume of water an object displaces in the water by its own weight.
- Water pressure increases with depth.
- Parts that work together to effect movements and transfer of force is shown by a kinematic chain.
- Unconstrained linkages can move in any direction.
- Constrained linkages form a mechanism, and motion of one part becomes predictable in its effects on other parts.
Strength of materials
how much load a weight-bearing structure can carry (ie, resists forces applied to it). Direction of applied force matters, because objects can respond differently to different types of stresses.
force presses down on an object.
forces stretch an object
forces slide sections of an object across one another.
- causes bending of column; forces greatest near surface.
- Therefore, bone surface features critical to resist forces acting on bone; may be larger than otherwise predicted.
Tensor fascia lata muscle and long tendon
- (iliotibial tract)
- =brace when entire trunk weight supported asymmetrically on one leg during locomotion. Brace prevents femur from beding during unsupported phases of striding in humans, and reduces tension in bone, which might cause failure. Also works in quadrupeds although using different structures.
begins with a microfracture that lengthens rapidly. Stress waves precede the fracture that causes the concentrated force to spread where material composition changes as the materials "give" slightly. When the sharp tip of the fracture meets the boundary, it is blunted and the fracture propagation is stopped.
causes by intermittent stress.
Atrophy of bone
can be caused by constant pressure (pressure erosions; ie, aneurysm or from lack of tension when immobilized in a cast.
on bone by a cradle board cause deformation.
causes change in shape of bones.
of bone (ie, Rickets) from calcium deficiency remains throughout life of individual in spite of possible remodeling later when normal mineral amounts available.
Trajectories of stresses
compensated for by internal structures of bones and other supporting materials, biological or not.
Bone can be remodeled
When shaft subjected to new, repeating, intermittent stress, it undergoes physiological process that thickens and straightens to compensate for new stress. Remodeled bone is again straight, but with thicker walls to withstand additional stress.
Blood flowing in opposite directions transfers heat form outgoing to returning blood to conserve body heat at core.
A vessel with deoxygenated blood passes across an air capillary carrying fresh air, causing blood O2 levels to rise stepwise.
- Where each eye conical field overlap, both "see" object (=stereoscopic) allows distance estimation =depth perception.
- Predators tend to have a greater overlap of visual fields, and therefore more depth perception than herbivores with eyes on sides of head that reduce the depth perceptive field, but increase the overall field of view.
- sharp focusing of a visual image onto the retina
- Farsighted - image focuses behind retina.
- Nearsighted - Image focuses ahead of retina.
Bending of light while passing from one fluid medium to another. Refractive indices differ between air and water, so eyes mainly selected to work in one or other.