Published online 6 May 2005
Published in Soil Sci Soc Am J 69:927-929 (2005)
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
Comments and Letters to the Editor
Response to "Comments on ‘Simultaneous Measurement of Soil Penetration Resistance and Water Content with a Combined Penetrometer–TDR Moisture Probe’ and ‘A Dynamic Cone Penetrometer for Measuring Soil Penetration Resistance’"
Rubismar Stolf*,a,
Klaus Reichardt
,b and
Carlos M. P. Vaz
,c
a Univ. Federal de Sao Carlos Centro de Ciências Agrárias Campus Araras SP, Brazil
b Center for Nuclear Energy in Agriculture Univ. of São Paulo Piracicaba SP, Brazil
c EMBRAPA Agricultural Instrumentation Sao Carlos SP, Brazil
* rubismar{at}cca.ufscar.br
In their letter, Minasny and McBratney (2005) review the physics of the dynamic penetrometer and question the presence of a linear constant predicted by Stolf (1991), summarized in Stolf et al. (1998), and adopted by Vaz and Hopmans (2001). This term takes into account the weight of the penetrometer by unit of cone area in the calculation of the soil dynamic resistance.
The approach of Minasny and McBratney was already presented in Stolf (1991) that compared both theoretical derivations (with and without the weight of the penetrometer). Consider the dynamic penetrometer (Fig. 1), initially with the mass of impact (M) lifted to a height h above the anvil (plate of impact). Assume that the penetrometer, before the mass M is lifted and dropped on the anvil, is at equilibrium with the indented soil surface. When the hammer strikes the anvil, the frame (mass m) moves together into the soil. The energy (E) applied by the action of dropping the hammer is
 | [1] |
where g is the constant of gravitational acceleration. However, is it the total energy of the system? This is the main scientific question in the whole discussion.
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Fig. 1. Dynamic penetrometer. Taking the Earth as a reference, mass M reaches the equilibrium h + x below its initial position, and mass m reaches the equilibrium distance x below its initial position.
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Review Fig. 1 in terms of energy balance from initial and final positions. Take the center of the Earth as the reference. Mass M has moved a distance h + x toward the center of the Earth. In addition, the frame, m, moved a distance x toward the same reference. Then, the total variation of the potential energy of the system will be 
P = Pfinal – Pinitial = Mg(h + x) + mgx. This is the more complete expression of the amount of energy. Rearranging terms,
 | [2] |
But, part of this energy is lost due to the impact as heat (internal friction). The more commonly used formula, known as the Dutch Formula (Sanglerat, 1972; Maquaire et al., 2002), admits an inelastic collision (maximum loss of energy). In this case, Newton's third law states that the remaining fraction of kinetic energy immediately after the impact (f) will be
 | [3] |
Then, the energy transformed in work will be W = Fx = fMgh (by Eq. [1]) or W = Fx = fMgh + (M + m)gx (by Eq. [2]), where F is the reaction of the soil. With soil resistance defined as R = F/A, where A is the cone base area, we have
 | [4] |
or
 | [5] |
where R is usually expressed as kgf (kilogram force) cm–2 (ASAE, 1976) or MPa, with the approximations that g = 10 m s–2 and 1 MPa = 10 kgf cm–2.
The constant term (M + m)g/A in Eq. [5] is, itself, the total weight of the penetrometer divided by the cone area (SP, static pressure),
 | [6] |
Take a dynamic penetrometer for which M = 4 kg, m = 1 kg, and A = 1 cm2. The penetrometer, before the mass M is lifted to height h, is at equilibrium with the indented soil surface. Then, the soil resistance must exceed the SP of 5 kgf cm–2 (0.5 MPa); otherwise, the penetrometer would never reach static equilibrium, and thus would not stop until the end of the shaft with no need for impact. In other words, it is not possible to measure soil resistance below this value. Comparing both equations, Eq. [5] previews the impossibility to measure soil resistance below the SP, whereas Eq. [4], defended by Minasny and McBratney (2005), does not.
The main problem with the comments by Minasny and McBratney (2005) lies in what was not analyzed. The aim of their letter is to calculate soil dynamic resistance, but they did not compare both formulas. Nowhere were we able to find at least one calculation of soil resistance. Table 1 shows three applications of this dynamic penetrometer to hard, medium, and soft soils. The value, R = 3.2 kgf cm–2 (simplified formula) is inconsistent (R < SP). If the soil resistance was 3.2 kgf cm–2, the penetrometer would never reach static equilibrium. It would not stop until the end of the shaft, even before impact. In conclusion, Eq. [4] is a theoretical simplification of Eq. [5]. Figure 2 makes a comparison between Eq. [4] and [5] for a wide range of R and x. The relative difference increases from hard to soft soils.
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Fig. 2. Comparison between soil dynamic resistance (R) calculated with Eq. [4] and [5]. Penetrometer: M = mass of impact = 4 kg, m = frame mass = 1 kg, h = height above the anvil = 0.4 m, A = cone base area = 1 cm2, f = remaining fraction of kinetic energy immediately after impact = 0.8, and SP = static pressure.
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Minasny and McBratney (2005) made the following comments for an impact penetrometer with M = 4 kg and m = 1 kg: "...makes the penetrometer create 0.5 J of energy for every centimeter of penetration, whereas of course simply moving the penetrometer cannot create energy. The fact that the system (M + m) moves to distance x is due to the impact energy of the hammer and is not an additional energy input to the system, but a loss of available energy." These comments were made without distinguishing between mass and weight (force), and therefore violates Newton's second law, which states F = ma = (M + m)g. See, the energy per centimeter is simply the weight of the penetrometer: 0.5 J cm–1 = 50 J m–1 = 50 N = (5 kg) (10 m s–2) = 5 kgf. That is, (M + m) is moving under the gravitational field! Then, (M + m)gx represents additional energy to be transformed in work of penetration, besides the impact. Ignoring this term is equivalent to suspending gravity during the penetration x (after impact). The term, (M + m)g, is a constant force; the lower the soil resistance, the greater the penetration (x), and the greater the resulting contribution in terms of work: W = Fx = (M + m)gx.
Consider the penetrometer, M = 4 kg, m = 1 kg, A = 1 cm2, length of shaft = 1 m, and SP = 5 kgf cm–2. If rested on the surface of a homogeneous soil with R 
5 kgf cm–2 (but slightly less), the penetrometer (M + m) will sink to the end of the shaft, 1 m deep. Then the work done by the penetrometer will be W = Fx = (M + m)gx = (50 N) (1 m) = 50 J or 0.5 J cm–2. Had the penetration reached 2 m, the work done by the penetrometer would be doubled. The lower the soil resistance, the greater will be the penetration, and more work will be done by the penetrometer.
To generalize, when dynamic or static penetrometers are used in the vertical position, it will not be possible to measure soil resistances below the SP, only above this pressure. The design of the best cone penetrometer implies a low SP to allow measurements in very soft soils. We contend that Eq. [5] derived by Stolf (1991) and criticized by Minasny and McBratney (2005) is correct, and that Eq. [4] is a simplification.
NOTES
klaus{at}cena.usp.br 
vaz{at}cnpdia.embrapa.br
REFERENCES
- ASAE. 1976. Soil cone penetrometer. p. 368–369. In 1975 Agricultural engineers yearbook. ASAE Tech. 313.1. ASAE, St. Joseph, MI.
- Maquaire, O., A. Ritzenthaler, D. Fabre, B. Ambroise, Y. Thiery, E. Truchet, J.P. Malet, and J. Monnet. 2002. Characterization of the profiles of superficial formations by dynamic penetrometry with variable energy: Application to Draix black marls, Alpesde-Haute Provence, France. Compt. Rend. Geosci. 334:835–841.[CrossRef]
- Minasny, B., and A.B. McBratney. 2005. Comments on "Simultaneous measurement of soil penetration resistance and water content with a combined penetrometer–TDR moisture probe" and "A dynamic cone penetrometer for measuring soil penetration resistance." Soil Sci. Soc. Am. J. 69:925–926 (this issue).[Free Full Text]
- Sanglerat, G. 1972. The penetrometer and soil exploration: Interpretation of penetration diagrams–Theory and practice. Elsevier, Amsterdam.
- Stolf, R. 1991. Teoria e teste experimental de fórmulas de transformação dos dados de penetrômetro de impacto em resistência do solo. Rev. Bras. Cienc. Solo 15:229–235.
- Stolf, R., D.K. Cassel, L.D. King, and K. Reichardt. 1998. Measuring mechanical impedance in clayey gravelly soils. Rev. Bras. Cienc. Solo 22:189–196.
- Vaz, C.M.P., and J.W. Hopmans. 2001. Simultaneous measurement of soil penetration resistance and water content with a combined penetrometer–TDR moisture probe. Soil Sci. Soc. Am. J. 65:4–12.[Abstract/Free Full Text]
