A Theory for Flake Creation
A Status Report of Research Begun April, 1997

Tony Baker
December 21, 2003

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Introduction
In April 1997, I became interested in the mechanics of flake creation. I purchased some mechanical engineering software in 1998, modified it for my purposes, and began attempting to understand flake creation. Subsequently, I wrote status reports about my work in November 1998, September 1999, March 2000, and November 2001. Each report represented my understanding of flake creation at that writing. Each kept some ideas presented in the previous reports and, at the same time, contradicted some of the other ones. Such is the nature of discovery.

Until the fall of 2002, the only computer program that I was using in the research was the one I had purchased and modified in 1998. That program was a static model and, therefore, it only allowed me to investigate pressure flaking. I knew this, but since pressure and percussion flakes are so similar with the exception of size, I was not too concerned about it being only a static model. In the fall of 2002 Bill Watts, a colleague of mine from my Texaco years wrote a number of dynamic programs that allow me to start to investigate percussion flaking. In September of this year, I wrote another status report. Four days after going public with it, I realized there were some major errors in it. So, I quickly set out to correct those errors. I discovered it wasn't that easy. What I thought I could correct in two weeks took me three months. This is that corrected version.

To close this section, I want to thank Bob Patten, Andy Pelcin, and Bill Watts. Each of these individuals has been involved in this research almost since its inception.

Vibration of Cores
Figure 1 represents a vertical, glass cantilever beam that is 1-inch long, 1/4-inch thick and firmly anchored on the bottom. (Click on Figure 1 if you haven't previously done so.) This cantilever beam can be visualized as representing a 1-inch wide, 1/4-inch thick biface core that is firmly supported at the edge opposite from the platform. If a force is applied to the platform of the core, it will bend as shown in Figure 2. In the real world this large amount of bending is impossible because glass is too brittle and will break. However, cores do bend when force is applied and the bending can be seen with magnification. Here the magnification is accomplished mathematically.

When the force is slowly removed from the core, it returns to its unbent shape, which is depicted in Figure 1. Again, Figure 2 is the bent shape and Figure 1 is the unbent or "at-rest-position" shape. If the force is removed instantaneously, the core will vibrate as in Figure 3. This vibration is identical to that of a tuning fork or a pendulum of a grandfather clock. Clicking on Figure 4 will cause the core to vibrate for only one cycle. Click on Figure 4 a few more times and watch the motion during one cycle. The thin, vertical black line in the middle of the Figure is the at-rest-position for the core. At the beginning of the cycle, the end of the core is on the right with no velocity. As it begins to move to the left and towards the at-rest-position it gains velocity. When it crosses the at-rest-position it has completed 1/4 of a cycle and is at maximum velocity. Past the at-rest-position, it begins to slow down as it continues to move to the left. At the far left, 1/2 cycle later, it stops and then begins moving back to the right, gaining velocity as it goes. Again as it crosses the at-rest-position, 3/4 cycle later, it is moving at its greatest velocity. Moving further to the right, it begins to slow down and finally stops at the far right and ends a single cycle. The time it takes this core to complete one cycle is 0.0004726 seconds, which is called the period of the vibration. Or, the core makes 2116 cycles in one second, which is its frequency. A frequency of 2116 cycles per second is well within the audible range of the human ear and, in fact, it lies within the range of the piano.

This period of the core does not vary with the amount of initial displacement. Figure 5 compares the vibration of the core for two different initial displacements. As can be seen, the time of a complete cycle is the same even though the red starting position is about half that of the black. This is extremely important because this means that the velocity of the end of the core is faster for the larger initial displacement. A pendulum on a grandfather clock behaves the same way. The period is independent of the displacement but the velocity is not. The period of the core is dependent on its shape, mass and material; removing flakes changes its shape and mass, and therefore its period. However, it does not change appreciably with the removal of a single flake so knappers are able to adjust their behavior gradually and subconsciously.

Pressure flaking is the application of a slowly increasing force. The force is applied so slowly that the entire core is able to bend or deflect in response to the gradually changing force. In different words, there are no inertia effects; the entire core and supports feel the pressure flaking force and respond to it. Figure 2 is an example of a load applied by pressure flaking. The entire core has experienced the force and the entire core has been deflected. Additionally, the amount of deflection is related to the amount of force that is applied. The more force, the greater the deflection. This is evident in Figure 5. The black response was created by mathematically applying a force twice that of the red response. It is the same core in each response.

So what determines how much force the knapper must apply to a core to initiate a crack when pressure flaking? Is it the muscles in his hands and legs? No, it is the platform. The platform strength determines how much force the knapper must apply to start a crack. If the strength is low, then little energy is added to the core and a short flake is the result. If the strength is high, abundant energy is added to the core and a long flake can result. Sometimes the platform strength is so high that the knapper can not overcome it and nothing happens.

Platform strength can vary for a number of reasons. If the platform is at an off-margin location, then it is stronger than a margin location. If the platform is on the margin, then platform preparation, such as grinding or polishing, determines its strength. Obviously, platform strength must not be too weak nor too strong, it must be just right. Therefore, it is one of several critical variables a knapper must manipulate while performing either pressure or percussion flaking. This is the reason Whittaker writes "platforms are the key to successful knapping" (1994:98). Patten concurs in his book with "preparing a stable platform is one of the most crucial skills a knapper can develop" (1999:39).

Figure 6 is an animation of the core in Figure 1 as the force is slowly applied to the platform. The force is applied at the location of the crosshairs and perpendicular to the platform face. The deflections are magnified 15,000 times. Click Figure 6 a couple more times and watch the movement of the platform. Also, note that at the end of the animation, the entire length of the core is experiencing deflection and this deflection is energy added to the core.

As stated above, if the force is gradually increased to the magnitude of the platform strength, then a crack initiates. In Figure 7, the crack initiation animation has been added. After the crack begins to propagate, the force needed to continue to separate the core from the platform is extremely small compared to that required to initiate the crack. To simplify this theory of flake creation, I assume this separation force is zero and the core is free to vibrate at its natural frequency.1 Figure 8 depicts the creation of an entire flake with this assumption. Basically, the crack is propagated by the core pulling away from the platform. Click on Figure 8 as many times as necessary to determine movement of the core and platform during the creation of this flake.

The movement of the platform during the creation of the flake in Figure 8 is nil. This animation represents a rigid impactor or pressure tool, which means it does not move after the crack begins. This is an example of the crack being created with only the energy that is stored in the core. There is no additional energy or movement added by the impactor after the crack initiates.

With the previous assumptions of a separating force equal to zero and a rigid impactor, I can make a statement about the time it takes to make the flake or the speed of the crack. Notice in Figure 8, the crack finishes at the same time as the core returns to the at-rest-position. The time interval from the beginning of vibration (initiation of the crack) to the core reaching the at-rest-position is of the period (0.0004726 seconds) or 0.0001182 seconds. Since the core and therefore the crack are 1 inch long, dividing the length of 1 inch by 0.0001182 seconds can approximate the average velocity. This velocity is 215 meters per second.2

As stated above, a rigid impactor makes the flake in Figure 8 because the platform never moves after the crack initiates. Rigid impactors do not exist in the real world and can only be created in the mathematical world as I have done here. In the real world, impactors deflect (compress) as they apply force to the core just as the core deflects when force is applied to it. When the crack initiates, the impactor tries to return to its at-rest-position just like the core does. The result is the impactor pushes the platform away from the core and helps to propagate the crack. Figure 9 is an example of non-rigid, real world impactor creating a flake.

The only difference between the flake created in Figure 8 and the one created in Figure 9 is impactor stiffness. All the other parameters ( angle of blow (AOB), platform angle, platform strength, etc) are identical. Figure 10 is an example of an impactor that is even less stiff than Figure 9, and again all the other parameters are the same. The flakes created in Figures 9 and 10 are feather flakes.3 The reader probably has also noted that the more flexible the impactor, the shorter and thinner the resulting flakes and the larger the bulbs of force are. These observations are correct as long as none of the other parameters are changed. However, the knapper can change the angle of blow and create a full-length flake with either of the flexible impactors in Figures 9 or 10.

Defining the Static and Dynamic Loading Modes
Energy can be applied to a core in the static mode or the dynamic mode. In the Vibration of Cores section, the entire discussion concerned the static mode. Pressure flaking is done in the static mode. Some percussion flaking is also performed in the static mode and some in the dynamic mode. So what is the difference between the two modes? How are they defined?

The answer to these questions can be seen in Figure 11. Basically, the motion of the core, not the motion of the platform, at the time the crack begins to form defines the two modes. An immediate reversal of the core's direction toward the at-rest-position is static loading. If the core continues in the same direction after the crack starts, then it is dynamic loading. For animations of these motions see Figure 12 for static loading, and Figure 13 for dynamic loading.

The conditions necessary for each are:
Static Loading Mode -- Loading time is greater than the period of the core.
Dynamic Loading Mode -- Loading time is less than or equal to the period of the core.

The above definitions are based on the loading time of the core and its period. That said, I would like to introduce Figure 14 to further explore these modes. Figure 14 shows the loading regions for the 3" wide biface core in Figures 12 & 13. On the horizontal axis is loading time, which is part of the above definitions. However, the vertical axis is width-to-thickness ratio instead of period. I choose to use width-to-thickness ratio because it directly relates to the period and it is easier to comprehend. The period of a core is a function of its material composition (type of rock, which is constant) and its morphology (width and thickness). Since most knappers attempt to thin their cores while preserving the width, width-to-thickness ratio for a constant core width (in this case 3") is a good proxy for the core's period.

I also wanted to use a more understandable proxy for loading time in Figure 14, but I could not find one. Unlike the period of the core, which is only a function of the core, the loading time is a function of platform strength, and the mass and stiffness of both the core and impactor. The knapper can't change the mass or stiffness of the core at any given stage, but he can definitely alter the platform strength. Additionally, he can change the mass and stiffness of the impactor. The most effective way to do this is to change the impactor's composition (rock, antler, bone, wood, etc.), size, and morphology (spherical, asymmetrical). To a lesser degree, the knapper can effect the impactor stiffness by varying the velocity of the blow and, in the case of asymmetrical impactors (billets), the attack angle can be altered.

Figure 14 also refers to Figures 15, 16, & 17, which are also cores with a width of 3 inches. However, their loading times are a constant 0.0002 seconds and their width-to-thickness ratios vary. With a loading time of 0.0002 seconds, it is very difficult to achieve static loading unless the core is extremely stiff. The core in Figure 15 is in the static region. It is 5 inches thick, which is a width-to-thickness ratio of 0.6. Conditions that this might represent are the earliest stages at the quarry where large irregular chunks are being impacted with spherical rock hammers of similar size.

Figure 16 represents a core a width-to-thickness ratio of 3 (1 inch thick) and is in the dynamic loading region. This width-to-thickness ratio is very common among the discarded cores at a quarry. Often these types are referred to as failures if one assumes they were on a reduction trajectory to becoming projectiles. (See Contrasting the Lithic Technologies of Mesa and Folsom.) These are also created with rock impactors that have similar masses as the core.

Figure 17 is the same core shown in Figures 12 & 13, which has a width-to-thickness ratio of 7. However, the loading time is five times faster than Figure 13, and 12 times faster that the core's period. The loading time is so fast in relation to the period that a strong, second harmonic has been introduced into the vibrating motion. Now the core actually reverses direction several times during its fundamental period of 0.00248 seconds. Click Figure 17 several more times and notice these reversals. These reversals cause hinge flakes, which are also very common at quarries because of the use of rock impactors. I will have more to say about hinge flakes in a later section.

Energy -- The Engine of Crack Propagation
Flakes are created because there is energy stored in the core prior to the crack initiating. The more pre-crack energy stored, the larger the flake can be. Figure 6 depicts the core bending prior to the crack initiating. This bending is the storing of the energy. Also, remember that platform strength determines when the crack initiates. As soon as the impactor force exceeds the platform strength, be it a pressure force or percussion force, the crack will start as it does in Figure 7.

Three variables determine how much pre-crack energy is added. These are platform strength, loading time, and the core itself. Strong platforms add more pre-crack energy than do weak platforms. Loading times can cause increases or decreases in pre-crack energy. Other variables being equal, flexible cores acquire more pre-crack energy than stiff ones. So how do these variables relate to each other in a manner that can be understood?

I struggled with this problem for several years. Finally, one day when all the celestial bodies happened to align just right, I discovered Figure 18, which is the normalized energy added to a core versus the normalized loading time. The two images in Figure 18 are the same, except the lower image is an expanded view of the red box in the upper image. The horizontal axis is normalized loading time (NLT), which is loading time divided by the period of the core. The vertical axis is normalized energy (NE) added, which is the pre-crack energy added to the core divided by the pre-crack energy added if the platform was loaded by pressure flaking. Figure 18 can be used for pressure and percussion. It can also be used for any size core that is supported on the far edge from the platform.4 Finally, it applies to all platform strengths.

A discussion of the curve in Figure 18 is in order to understand further its significance. Let's begin far to the right of the top image at a NLT of 1000.0 or so. A NLT of 1000.0 is a loading time 1000.0 times longer than the period of the core. This is the region of pressure flaking and the NE curve is flat at a value of 1.0. And, it should be because the pre-crack energy added by pressure flaking and divided by the same value is 1.0. This is the definition of the NE.

Moving to the left or to lower values of NLT in Figure 18, the NE curve begins to oscillate around the value of 1.0. At NLT around 10.0 this oscillation is between 0.97 and 1.03, which is insignificant in the knapping process. Continuing to lower values, the oscillating amplitude of the NE increases to significant values between 0.8 and 1.2 for NLT values between 1.0 and 2.0. At a NLT of 1.0, the NE is 1.0. Also, this is the transition between static and dynamic loading.

Crossing into the dynamic region where the NLT is less than 1.0, the NE added to the core increases to the peak value of almost 1.6 in Figure 18. This is 1.6 times the energy added during pressure flaking. This peak occurs at a NLT of 0.75. Then the NE curve starts to fall rapidly. It is back to 1.0 around a NLT of 0.5 and it is 0.0 and a NLT of 0.0

All the examples in Figure 14 plot on the NE curve in Figure 18. These five examples represent three different cores and three different loading times. Notice how Figure 18 separates and accounts for all these conditions.

Figure 18 is an explanation of the mathematical connection between pressure and percussion flaking. However, it can be misleading because the reader might think that percussion knapping occurs all along the NE curve. I don't believe this is the case. The knapping process begins at the quarry with a hard rock impactor and chunk of flakeable material. When I run values that represent these real world conditions in my computer programs, the percussion work always occurs at NLT values of 2.0 or less. I suggest that when the rankest rookie smashes two rocks together, the NLT is less than 2.0. The experienced knapper has learned to perform his knapping near a NLT of 0.75 with little variation from flake to flake. A NLT of 0.75 is the location of peak energy input into the core.

Removing each successive flake while maintaining a NLT of 0.75 is not easy, nor is it like shooting at a fixed target. Shooting at a fixed target requires the shooter to repeat everything exactly the same way from shot to shot. Flake removal is a moving target. It is a moving target because the period of the core is increasing as the core is becoming thinner. If the knapper repeats everything exactly the same way from blow to blow, he will be moving to the left in Figure 18. His flakes will change to step flakes because he will progressively apply less and less energy to the core with each flake removal. To compensate the knapper slows down his blow, which slows his loading time, and moves back toward the peak. However, ultimately the knapper will not be able to slow the blow any further because his impactor will have insufficient energy to exceed platform strength and initiate a crack.

The next thing the knapper does is subconsciously concede that he can no longer operate at peak energy input and increases his angle of blow (AOB), by moving the support or by selecting or creating a more acute platform angle. This larger AOB will cause the flake to feather out just before the crack would have stopped in a step termination. Additionally, he will select or create stronger platforms so he can still get an acceptable size flake. The effect of these two changes is to create feather flakes with strongly wedge shaped cross-sections. If these wedge shaped flakes are acceptable to the knapper, he will continue until the NLT value drops below 0.10+ and then short, unacceptable hinge flakes start to occur. At this point the knapper generally abandons the core or switches to pressure knapping.

The important point in the above scenario is that the impactor was never changed. If the impactor had been changed to softer material, such as antler, bone or wood, then the core could have been further thinned. A soft impactor changes the NLT value significantly. If a knapper was to change from a hard rock impactor that is operating at NLT=0.75 to a soft impactor and hold all other parameters the same, the new NLT value would be greater than 0.75. In fact, I don't believe a soft impactor deployed against a quarry chunk with a width-to-thickness ratio of approximately 1.0 can be made to operate at the peak energy input of NLT=0.75. Only when the width-to-thickness ratio of the core becomes larger will the soft impactor begin to operate at the peak value. When the soft impactor is operating at the peak, the hard rock impactor is making steps or hinges if all the other parameters were the same.

The Archaeological Record and Copper Impactors
The archaeological record from large quarry sites contains many bifacial cores that are whole and fragmentary. It has been my observation that these cores, regardless of the quarry location around the world, have two common traits. They have step and/or hinge flake scars and they rarely exceed a width-to-thickness ratio of 4.5. These cores are a signature of a quarry and I define them as quarry artifacts.

Quarry artifacts are the products of hard rock percussion on off-margin platforms. As discussed above the knapper begins the reduction of a chunk or spall of lithic material with a hard impactor and the NLT is in the range of 0.75. This is maximum energy input. As the core is reduced, the knapper doesn't change his impactor and, therefore, the NLT is decreasing. As the process continues steps flakes and ultimately hinges flakes start to occur. At this point the width-to-thickness ratio is still below 4.5. The knapper could change to a soft impactor (antler billet) and continue to reduce the core, but instead he chooses to abandon the core. The reason is that lithic material and hard impactors are abundant. Soft impactors are not abundant, and they are high maintenance tools in that they have to be continually refurbished and often replaced.

Away from the quarry, lithic material has a much higher value to the knapper. Now, the knapper will employ a soft impactor and choose platforms on the margin to conserve lithic material. By using a soft impactor, he can raise the NLT and further thin the core without step and/or hinge flakes occurring. With some skill width-to-thickness ratios of 7.0+ can be achieved.

Many modern knappers use copper impactors for their percussion work. Copper is closer to hard rock than it is to antler or wood, and therefore its NLT's are closer to hard impactors. It will yield step and/or hinge flakes sooner than soft impactors. Therefore, to avoid steps and hinges, the copper knapper will switch to pressure at an earlier stage of reduction (smaller width-to-thickness ratios) than the soft impactor knapper.

Final Remarks
The theory of flake creation presented in this web page has used biface cores in all the examples. This does not imply that it is not applicable to blade or other cores, because it is. The biface core is just a better textbook example because it passes through a wider range of flexibility than does the blade core. For example, I have observed that exhausted blade cores rarely exceed a length-to-thickness ratio of 2.0. However, as discussed previously, exhausted biface cores found at quarries (the quarry artifact) approach a width-to-thickness ratio of 4.5. Assuming that both blade and biface cores begin at a ratio of 1.0, bifaces are thinned twice as much as blade cores and, therefore, pass through a greater range of flexibility.5

Blade cores are so stiff in relation to the impactor that creating the second harmonic vibration in the core is almost impossible. That said, one would think it would be impossible to create hinge flakes on a blade core. However, look at Figure 19. This is a blade core with three ugly hinge flake scars. This probably happened because a soft, billet impactor was used (Jacques Pelegrin, personal communication 2003). Unlike the biface/hard hammer collision where the biface is the flexible member, the blade core/billet impact has the billet as the flexible member. Therefore, the second harmonic responsible for the hinge flake occurs in the billet and not in the core. This occurs when the blade core's mass is decreased to the point that the knapper has to swing the billet faster than normal and hold the core tighter than normal in order to get significant energy into the core (Jacques Pelegrin, personal communication 2003). The loading time is reduced and ultimately hinge flakes will begin to occur as in Figure 19.

Finally, the theory presented in this web page was derived from the output of several computer models, the archaeological record, and the products of the modern knapper. These three items had to be stitched together with logic and common sense and therefore, the theory may be partially or total incorrect. I sincerely hope someone attempts to test and challenge it.

References
Cotterell, Brain and Johan Kamminga
1987The Formation of Flakes. American Antiquity 52:675-708.
Patten, Bob
1999Old Tools--New Eyes: A Primal Primer of Flintknapping. Stone Dagger Publications, Denver.
Pelcin, Andrew W.
1996Controlled Experiments in the Production of Flake Attributes. Ph.D. Dissertation, Department of Anthropology, University of Pennsylvania, Philadelphia. University Microfilms, Ann Arbor.
Whittaker, John C.
1994Flintknapping: Making & Understanding Stone Tools. University of Texas Press, Austin.
Van Peer, Philip
1992The Levallois Reduction Strategy. Monographs in World Anrchaeology No. 13, Prehistory Press, Madison.

Notes

1 The assumption of a separation or propagation force of zero is obviously not correct because chemical bonds are broken as the crack is propagating and this requires the consumption of energy. However, after hundreds of FEA runs, it appears the energy to break the chemical bonds is very minute compared to the energy required to flex the core and overcome the platform strength.

2 The average speed of 215 meters per second is too large because the calculation assumes the vibrating core thickness does not change as the flake is made. This is obviously incorrect. Look again at Figure 8. The flake being removed is reducing the 0.25-inch thick core to a thickness of 0.195 inches. This changes the period of the core vibration. A core that is uniformly 0.195 inches thick and 1 inch long will have a period of 0.0006059 seconds or about 30% longer. With this longer period, the average speed of the crack would be 168 meters per second. So the actual average speed of the crack in Figure 8 lies between 168 and 215 meters per second.

3 In Figures 8-10, the computer program was stopped just before the next movement would have separated the flakes from the cores. The computer magnification greatly distorts the images.

4 Figure 18 was derived from a mathematical model of a cantilever beam. A cantilever is a beam that is supported on only one end. A diving board is a cantilever beam. The biface in Figure 1 is a cantilever beam.

5 Blade cores being thinned to only a length-to-thickness ratio ratio of 2.0, while biface cores are thinned to a width-to-thickness ratio of 4.5, suggests that less rock is wasted at the quarry with biface cores. This contradicts the old adage that blades yield more edge per pound of rock than biface cores.


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