Biology 202 Egg Strength Winter 2011
The evolution of the amniotic egg is considered one of the major evolutionary events, heralding full independence from water and the conquest of land by vertebrates. Although first evolving with early amniotes, it is in the form of the bird egg that most people are acquainted. From a mechanical point of view, the avian eggshell is an impressive example of natural engineering. It provides the outer capsule of an almost fully self-contained environment that supports the mass of the developing chick and prevents it from being crushed (Ar et al. 1979).
The shell is a composite of a biological ceramic, calcite, and 2-4% of organic fibers (Vincent 1990). The calcite component in the shell makes it brittle. The distribution of calcite crystals is not homogeneous and the shell is porous permitting respiratory gases to pass through it. The morphology of the shell materials is highly complex and mechanically enigmatic (Vincent 1990). However, the geometry of the eggshell makes it remarkably resistive to external loading.
To crack an egg, a person turns the egg on its side and hits it on the edge of a hard surface. To package and protect the egg, it is placed on end in a carton. It might be assumed that the force required to break an egg is different depending on where the force is applied. Indeed in Gulliver's Travels (1726), the two great empires of Lilliput and Blefuscu went to war over which was the proper end of an egg to break (Swift 1974).
The mechanics of an arch permits great structural strength with an economy of materials (Vogel 1988). The dome is an arch rotated about its vertical axis (Giancoli 1991) and, as architects are familiar, large roofs can be supported without internal bracing (Burke 1985). Domes are stiffer than arches, because of their three-dimensional structure (Vogel 1988). Arches and domes are statically stable and they can support large loads, because their walls are mainly under compression (Giancoli 1991). However, the magnitude of forces necessary to stabilize an arch varies with its geometry. The pointed (Gothic) and parabolic arches (Figure 1) are more vaulted and require lower stabilizing forces when subjected to a compressive load than a simple semicircular arch (Giancoli 1991). Similarly, a highly vaulted dome (i.e., low radius of curvature) is stronger than a flatter dome (i.e., high radius of curvature; Vogel 1988).
The eggshell from a chicken is ellipsoidal with high-vaulted, domed ends and sidewalls with high radius of curvature (Figure 1D). Based on analysis of arches and domes, there should be differences in the strength at the ends and sides of the shell.A hypothesis would be that more force is necessary to break an egg on its end than on its side.
In this experiment, students will examine the structural mechanics of the chicken egg. Students can specifically test if there is a difference in where a force is supplied to crush the egg. Is more force required to break an egg on its highly domed end than the flatter side? This experiment integrates principles of biology, physics, and engineering.
Methods
An egg breaking apparatus is designed for the application of force to the surface of an egg. The top and base of the apparatus are constructed of 3/4-inch (1.9 cm) wood cut into triangles, which are seven inches (17.8 cm) to a side. Each corner of the base is fitted with one 1/4-inch (0.6 cm) wooden dowel of 9 inches (22.9 cm) in length. Corresponding to the position of the dowels, 7/16 inch (1.11 cm) holes are drilled in the corners of top piece that allows it to slide guided by the dowels. Vasoline can be used to lubricate the dowels. A high-walled bucket or beaker that does not touch the dowels will sit on the top piece of the apparatus. The combined weight of the top piece, bucket, 1 kg mass and sand poured into the bucket will serve as the force used to crush the egg. Place a glass jar between the egg and the platform to elevate it and reduce friction.
Eggs to be tested should be within the same size category (i.e., small, medium, large, extra large). The eggs are to be divided into two equal treatment groups. One treatment group will be tested to determine the force necessary to break the end of the egg (End); whereas, the second treatment group will be used to measure the breaking force of the side of the egg (Side).
Prior to testing, the lengths of the major and minor axes of the eggs should be measured with calipers. To provide an indication of the geometry of the end and side of the eggs, a dome coefficient is tobe calculated as the ratio the dome height to the dome diameter (Figure 2). The dome coefficient for the side of the egg is 1/2 the short axis length divided by the long axis, and 1/2 the long axis length divided by the short axis length for the top of the egg.
To determine breaking force, an egg is to be placed on a Petri dish on top of a glass jar on the platform. The egg will be positioned on either its end or side, depending on the treatment group. The egg will be positioned on the apparatus base so that the top piece of the apparatus contacts the surface of the egg. The 1 kg mass is placed in the bucket and sand is poured slowly into the bucket until the eggshell collapses. The combined mass of the top piece, bucket, 1 kg mass and sand are measured on a top-loading balance. The force, in Newtons (kg m s-2), to crush the egg is computed as the mass in kg times the gravitational acceleration (9.80 m s-2).
Comparisons of mean breaking strength between the end and side of the chicken and quail eggs can be statistically calculated.
Variation on Original Study
Use quail eggs, hard boiled, eggs without insides, small, medium, large, and extra large.
Student Responsibility to Report
We will pool the data. Each table (group) will obtain dome coefficients and crushing mass for six End eggs and six Side eggs. Each student is to turn in a Plot of force in Newtons vs. end or side of egg with mean and range indicated. The plot should look like Fig.3 and include an informative figure caption. Also report the average (and range) of the dome coefficients in a table with an appropriate caption.
Literature Cited
Ar, A, H. Rahn, and C.V. Paganelli 1979. The avian egg: mass and strength. Condor 81: 331-337.
Burke, J. 1985. The Day the Universe Changed. Boston: Little, Brown and Co.
Giancoli, D. C. 1985 Physics. Englewood Cliffs, NJ: Prentice Hall.
Swift, J. 1974. Gulliver's Travels. Franklin Library: Franklin Center Library.
Vincent, J. 1990. Structural Biomaterials. Princeton Univ. Press, Princeton.
Vogel, S. 1988. Life's Devices: the Physical World of Animals and Plants. Princeton: Princeton University Press.
Note: calipers, jars, vasoline, scales, 1 kg. weights.
Thanks to Frank Fish Westchester State University, Pennsylvania
Figure 1
Figure 2
Figure 3