Section 2.



There are two types of lead acid batteries generally used for vehicle applications  the ordinary automotive battery (used for starting, lighting, and ignition) and the traction battery used to supply motive power for electric vehicles. Automotive batteries are designed for infrequent, very high current drains of short duration, and recharging begins as soon as the engine reaches operating speed. Traction batteries, on the other hand, are designed to be discharged continuously at relatively moderate current drains because there is no practical way to recharge the battery during operation. The stored charge of a traction battery, therefore, runs steadily down from its starting condition until the battery is recharged. A reasonable service life from such a battery might be considered as 1000 to 2000 cycles of discharge and charge; and typical life spans for industrial batteries, properly used and cared for in fork lift trucks, are about 5 years, sometimes even longer.

Figure 4 shows typical charge/discharge characteristics for batteries used in two common commercial applications  a taxi and a fork lift truck, both used in 2-shift operations.

How a Lead Acid Battery Is Made

The lead acid battery is made up of several identical cells, each of which contains two plates, one positive, the other negative. Both plates are immersed in an electrolyte that is a mixture of sulfuric acid and water.

Two types of cell construction are common: flat plate and tubular plate. The overall functions of the two types are identical, but their mechanical construction and performance differ slightly.

In a flat plate cell (Figure 5), each positive plate is a cast metallic lead frame which contains the lead dioxide active material. The negative plates contain spongy metallic lead active material within a similar grid structure. Positive and negative plate areas are usually identical.

In a tubular plate cell (Figure 5), the positive plates surround lead alloy spines. The lead dioxide is in close contact with the spine over its entire length, and is retained by a special sleeve. Negative plates are of spongy metallic lead in a grid form identical to those in flat plate cells.


Figure 4: Battery Charge/Discharge Cycles in Two Commercial Applications



Figure 5: Typical Flat Plate and Tubular Plate Cell Construction



In either case, the cell is filled with electrolyte, which is slightly heavier than water. The ratio between the weight of a given volume of electrolyte and the same volume of water is the specific gravity of the electrolyte.

Figure 5 shows how a typical industrial cell is assembled. In order to provide sufficient current output (amperes) each cell consists of many plates (for example, 11 positive and 12 negative). Because each positive plate is positioned between two negative plates, there is always one fewer positive than negative. The positive plates in each cell are connected in parallel to provide a positive bus of the required current output, which is connected to the positive terminal of the cell. Similarly, the negative plates are bussed and connected to the negative terminal.

The cells are connected by external metal straps that hook them into a series circuit ... a circuit in which the negative plates of one cell are connected to the positive plates of the next, so that the voltages of all cells are added to provide the total voltage of the battery. Typically the cells are numbered in sequence beginning with the cell containing the positive terminal of the battery (number 1) and ending with the cell containing the negative terminal. (Figure 6.) There can be any number of cells in a battery, but the numbers most commonly used are: 3, 6, 9, 12, 15, 16, 18, 20, 24, 30, 36, and 40.


Figure 6: Battery Cell Strapping and Numbering



Battery rating information is generally displayed in coded form, stamped into the lead of the first negative terminal or on a nameplate on the side of the battery. As an example, the code for a particular battery might read as follows:







of cells


Cell Type


Capacity per

Positive Plate

Total Number

of Plates

Per Cell

(5 Positive, 6



The ratings for this battery are:

Voltage: 12 cells 2 volts each = 24 volts

Capacity: 11 - 1 positive plates 85 Ah each  = 425 Ah.




The electrolyte in a lead acid battery is a mixture of sulfuric acid and water. Sulfuric acid is a very active compound of hydrogen, sulfur, and oxygen. Its chemical formula is H2S04. In water, the sulfuric acid molecules separate into two ions, hydrogen and "sulfate," the latter of which is made up of sulfur and oxygen atoms. Each sulfate ion contains two "excess" electrons and each therefore carries two negative electrical charges. Each hydrogen ion, having been stripped of one electron, carries one positive electrical charge.

Because sulfuric acid is highly reactive, it ionizes almost completely and so there are very few fully assembled molecules of sulfuric acid in the electrolyte at any instant. Furthermore, the ions are in constant motion, attracted and repelled by one another, by the water, and by any impurities in the mixture. This constant random motion eventually causes the ions to diffuse evenly throughout the electrolyte. If any force disturbs this even distribution, the random motion eventually restores it. However, since the electrolyte is contained in a complex structure of cells, redistribution takes a relatively long time. This fact turns out to play a key role in our ability to measure the exact state-of-charge of the battery at any instant, as will be shown later.


In sections of this book. current is discussed in conventional terms as flowing from the positive to the negative; while. in other sections. it is discussed in the electrochemist's terms as flowing from the negative to the positive.


Figure 7: Schematic Representation of Reactions at Negative and Positive Plates

Producing an Open Circuit Voltage

The chemical reaction between the sulfate ions and the spongy lead of the negative plate produces lead sulfate, a compound that does not dissolve in water. This reaction frees two electrons and thereby produces a net negative electrical potential at the negative plate. (Figure 7.)

The presence of these free electrons slows down the chemical reaction at the negative plate because their negative charge repels other negatively charged sulfate ions. Fewer ions can then reach the negative plate to react with the spongy lead to form more lead sulfate. The overall reaction cannot continue very long, therefore, unless the excess electrons are permitted to leave the negative plate.

Meanwhile, at the positive plate, other sulfate ions react with the lead of the lead dioxide to produce lead sulfate; at the same time, the hydrogen ions of the acid react with the oxygen of the lead dioxide to form water. This combination of reactions produces a net positive potential at the positive plate. (Figure 7.) Here, too, the reaction can only continue as long as the electrical conditions are right. Within a short time, the supply of free electrons in the metal of the positive terminal is used up and no further chemical change can take place unless more are supplied.

The difference between the two potentials at the plates is the open circuit voltage or electromotive force (emf) of the cell. This emf (about 2.1 volts) will remain unchanged as long as no path is provided for the excess electrons to leave the negative plate and no source of electrons is provided for the positive plate. In this condition, there is little or no chemical activity in the cell, which means that a charged cell can be stored for a fairly long time without significant loss of energy. The open circuit voltage typically will drop by less than a millivolt (0.00lV) per day, during storage, if there is no loss of electrolyte  a process referred to as "self-discharging."

Producing Current

The available source of electrons to make up the deficit at the positive plate is, of course, the excess of free electrons at the negative plate. Since these free electrons are produced by the reaction between the acid and the lead, the total number of free electrons available is set by the amount of acid and lead available to react. A similar limitation exists for the positive plate; the total number of free electrons it can absorb is set by the amount of acid and lead dioxide available to react.

Since any flow of electrons is a transfer of charge, the total amount of charge stored in the cell is established by the total amounts of plate material and sulfuric acid available to react. The total amount of charge stored in the cell determines the capacity of the cell.

If a wire is connected between the two plates, the excess electrons instantaneously rush from negative to positive. This electron current * is very high because the wire is a short circuit between the terminals. If the wire is very thick (has no resistance at all), the total number of electrons transferred is determined only by the amount of electrolyte that has reacted  and continues to react - with the two plates. The net charge transfer is 2 electrons per molecule of acid. Since the number of molecules of acid is inconceivably large, a gigantic current could flow between the shorted terminals, transferring nearly all of the cell's stored charge from one terminal to the other in a very short time.

If electrical resistance ... a load ... is connected between the terminals, then the current is limited by the resistance of the load, and the cell's charge is transferred from terminal to terminal, via the load, at a slower rate, i.e.; a smaller electron current. For a typical traction cell, the current can be hundreds of amperes. This current will flow as long as the load is connected and as long as there is active material left in the cell to sustain it.

Since no physical process is perfect, the electrolyte/plate reactions offer resistance to this internal current and therefore lose some of the transferred energy in the form of heat. The electrical effect of this internal resistance of the cell appears as a loss of potential (a voltage drop) at each plate. The cell's total voltage under load is therefore less than its open circuit voltage. The amount of energy lost to this internal resistance depends on the load current and on the concentration of acid in the cell ... especially the acid concentration at the positive plate. The larger the load current, the greater the loss of energy. Also, the lower the acid concentration at the plates, the higher the internal resistance of the cell.


When discussing the electro chemical reactions in a battery, it is useful to refer to electron flow as current.


When current is produced by the cell, acid, lead dioxide and lead are converted to lead sulfate and water. Each acid molecule that reacts is no longer part of the electrolyte. This process, by reducing the concentration of acid in the water, gradually reduces the ability of the cell and leaves less energy in it.

In the design of batteries, the amounts of acid and plate-active materials are balanced so that the release of energy relates to the rate at which current is likely to be drawn. Batteries designed for low-rate applications, such as for storage in solar power systems, contain a larger amount of acid in proportion to plate-active material. They are designed to be plate-limited when used beyond their rated capacity. No plate materials will be available for releasing usable energy.

Batteries designed for high-rate applications, such as automotive ignition, etc., have a smaller amount of acid in proportion to plate-active material. They are designed to be acid-limited when used beyond their rated capacity.

As acid concentration becomes too low, a cell becomes incapable of releasing usable energy at the rate for which it was designed. Additional energy can only be drawn from it if the current rate is reduced. As it is driven to excessively low acid concentrations (through deep discharging), the coatings of lead sulfate produced by the chemical reactions at the plates will not reconvert. Upon charging, acid concentration is restored and plate coatings will again reconvert.

The traction battery used with fork lift trucks falls between the automotive and storage battery in its proportion of acid and plate-active material. It is generally considered to be acid-limited for rates exceeding the 6-hour capacity.


The cell's state-of-charge is determined by the amount of active material available to sustain a usable current flow through a load. At the outset, all of the active material is available and the cell is fully charged. When it can no longer produce usable current, the cell is fully discharged. At any point between these two extremes, the state-of-charge of the cell is expressed as a percentage of the total difference in charge between the fully charged and fully discharged states.

Since the state-of-charge is set by the availability of active material in the cell, it is conventional (but not alone sufficient) to define the cell's state-of-charge in terms of the specific gravity of the electrolyte. As defined above, specific gravity, a measure of density, is the ratio of the mass of the mixture of sulfuric acid and water in the electrolyte to pure water at a specified temperature. It is common to speak of, for example, 1300 SG in lieu of 1.300 specific gravity: a convenience simply achieved by multiplying 1.300 by 1000. For the purposes of this book, from this point on, specific gravity measurements shall be expressed in SG form. All SG measurements are corrected to + 25°C.

The relationship between state-of-charge and specific gravity is usually shown in a form similar to Figure 8. Note, however, that this illustration does not take into account the dynamic activity inside the cell while current is flowing. It shows only the long-term average relationship when the load has been disconnected and the sulfate ions have had a chance to diffuse evenly throughout the cell.


Figure 8: Stabilized SG for 2 Cell Types Vs State-of-Charge at the 6-Hour Rate




The time required for this diffusion process to be completed varies according to the rate, depth and length of discharge and is different in cells of different design. Figure 9 shows this effect as measured on a typical cell that has been discharged at a moderate rate. In this test, it took more than 16 hours for specific gravity to fully stabilize.

Since the lead sulfate forms at the plates, the specific gravity of the electrolyte is lowest near the plates and highest farther from them. Measuring specific gravity during or shortly after discharge actually provides false information about actual average specific gravity, with an error factor that depends on the depth and duration of the cell's recent discharges. *

Determining Battery Capacity

Battery capacity is determined through manufacturer testing. Manufacturers have test procedures which are utilized to establish the hour rate and ampere-hours of their batteries. Prior to making a capacity measurement, the battery is fully charged (typically 1290-1300 SG). Then it is connected to a load that draws a desired current. The battery's output current and its voltage are monitored continuously for the specified time. A conventional test setup is shown in Figure 10. In this case, the battery capacity was intended by its manufacturer to be 960 ampere-hours at the 6-hour rate; that is, the battery is designed to be capable of delivering 160 amperes for 6 hours. The final (end point) voltage is specified as 30.6 volts (1. 7 volts per cell). The resistance of the load in our hypothetical test setup is adjustable from 0.23 ohms to 0.19 ohms.

At the start of the test, the resistance is set to 0.23 ohms (160 amperes at 36.4 volts). As soon as the battery delivers some of its charge, its output voltage begins to fall. To keep the load current at 160 amperes, the load resistance must therefore be reduced slightly. This adjustment of the load resistance is continued until the battery output voltage reaches 1.7 volts per cell (load resistance of 0.19 ohms at 160 amperes). For this battery of 18 cells the end point voltage is 18 1.7 or 30.6 volt at 100% discharged.


*In practice. the daily measure of specific gravity is made at the same point in the battery's operating sequence (for example, at the end of each shift). In this case, approximately the same conditions will have been reached when the measurement is made and the results will therefore be fairly consistent. Such measurements will, however, be offset from the true value of specific gravity by some unknown and uncompensated amount, which can be determined by letting the battery stabilize and remeasuring the specific gravity.


Figure 9: Time Required for SG to Stabilize During Discharge Rest Intervals



Figure 10: A Conventional Test Setup for Determining Battery Capacity



The end point voltage signifies, by general agreement, the practical, 100 % discharge of the cell. * The length of time it takes for this end point voltage to be reached is the "hours" part of the "ampere-hour" rating; the constant current, of course, is the "amperes" part.

In the U.S., traction batteries are usually specified at the 6-hour discharge rate. In other countries, a 5-hour rate is common. The rate is the constant current drain that depletes the battery's charge so that at the end of that many hours, the end point voltage across the load is only 1.7 volts per cell. For situations in which other discharge rates apply, manufacturers may specify other end point voltages ... some ranging as low as 1.2 volts at very high discharge rates or as high as 1.85 volt at very low discharge rates. A typical set of end point voltages is shown in Figure 11. In the U.S., traction battery data at various discharge rates is usually presented using 1.7 volts per cell as the 100% discharge end point.

Capacity and Discharge Rate

If we assume that the capacity of a typical 960 ampere-hour battery is unaffected by discharge rate, we would expect it to discharge in 3 hours with a current of 320 amperes (960 Ah divided by 320 A = 3 Hrs). Actually, at a current drain of 320 amperes, the final voltage of 1.7 volts per cell is reached after only about 2.5 hours. The capacity of the battery in ampere-hours and the discharge rate are not linearly related. For example, our typical battery delivered 160 amperes for 6 hours, which we call 100% capacity, but only 265 amperes for 3 hours, 17% less than might be expected, and 350 amperes for 2 hours, 27% less than expected. The point to keep in mind is that the heavier the continuous load on the battery, the less capacity it has. Figure 12 shows the manner in which discharge rate affects the capacities of two similarly rated batteries from two different manufacturers.


*For all practical purposes, a cell is discharged only to 80% of its capacity because energy drawn from the cell after that point causes voltage to drop at a steep and rapid rate. In the world of lead acid traction batteries and fork lift trucks, a battery is considered discharged at 80 %. while at 100 % discharge it is well into the area of deep discharge. It would seem prudent to simply term the 80% level as 100%. but it is not the province of this book to alter any such widely used convention.

For some street electric vehicle applications. voltages as low as 1.0 have been specified.


Figure 11: Typical End Point Voltage as a Function of Discharge Rate: (Valid when manufacturer rates battery with a current-dependent end point voltage, ([from Manufacturers' data].)



Figure 12: How Battery Capacity Varies with Discharge Rate



Capacity and Temperature at Electrolyte

Another important factor that affects battery capacity is electrolyte temperature. Generally speaking, the higher the temperature the more rapidly any chemical action will proceed. The speed with which the acid combines with the plate materials is much higher when the electrolyte is hot. Conversely, when the electrolyte is cold, the reactions move slower.

At high temperatures, the faster chemical action at the plates permits more material to take part in the chemical reactions, which is roughly equivalent to having more material available to react. Since battery capacity ultimately depends on the amount of material available to react, increasing the temperature of the cell increases its capacity. *

This effect is so pronounced that at the freezing point of water, capacity at the 5-hour rate is only 65% of capacity at 80 °F. (See Figure 13.) For this reason, any specification of battery capacity must state the temperature at which the specification applies.


*It is generally agreed in the battery industry that continuously high temperature can be related to grid deterioration of the plates. Considering 80°F as a normal temperature, for each 15°F of above normal, industry experts say that battery life will be reduced by half. A typical battery discharged al normal rates to 80% DOD at about 80°F (25°C) will show a raise of electrolyte temperature of about 12°F. To return the battery to normal, a cooling period of up to 12 hours may be necessary. Thus, manufacturers caution against using batteries two cycles per day. This does not allow time for cooling and results in reduced battery life.

State-of-Charge Measurements

The constant-current method outlined earlier (Figure 10) is the way in which batteries are evaluated at the factory to produce the specifications by which users select the correct battery

for any application. But once the battery has been selected and is installed on the truck, the user is interested in "state-of-charge" at any moment, as well as rated capacity. The standard capacity-measuring test is no help here because currents are constantly changing. Four techniques are used to measure state-of-charge:


Figure 13: How Battery Capacity may be Affected by Electrolyte Temperature.



Specific Gravity and Open Circuit Voltage


The open circuit voltage of a cell is a precise indicator of specific gravity when a cell is fully stabilized. And as such, the open circuit voltage is a precise measure of state-of-charge. Because open circuit voltage is determined solely by the concentrations of acid at the plates, it will not agree with specific gravity readings unless the acid is uniform everywhere in the cell. Then, measuring the open circuit voltage after stabilization is equivalent to measuring the specific gravity. This relationship is shown in Figure 14. The time required for stabilization can be hours, depending on the depth and duration of discharge and is different for cells of different design. Under laboratory conditions, Figure 14 is a valuable relationship; in practical applications, however, it is ambiguous at best. The unstabilized open circuit voltage will always read higher than at the equivalent point in Figure 14 if the cell has just been taken off the charger. Conversely, the unstabilized open circuit voltage will always be lower than at the equivalent point in Figure 14 if the cell has recently been discharged.

Figure 15 shows open circuit voltage of a typical cell measured at various times after disconnecting the load. In this test, the open circuit voltage rose rapidly but did not reach its stable value of 1.982 volts until more than 100 hours had elapsed. The peak of 1.990 volts reached after some 6 hours was not sustained.

Voltage under Load

Under test conditions like those shown in Figure 10, we can examine the way voltage under load is related to battery capacity. For example, let's assume that we are testing a traction battery with a capacity of 1050 Ah at the 6 hour rate.

At a moderate load of 200 amperes, we find that the voltage stays constant (within about 7%) for nearly 4 hours (actually 3.96 hours, as shown in Figure 16). Up to this point the battery has delivered 792 Ah, or 80% of its capacity.

If we repeat the test, but draw 400 amperes, the nominal voltage to 80% discharge holds constant to within about 8%, but for only about 1.6 hours (1.57 hours as shown in Figure 16). Up to this point the battery would only deliver 628 Ah, 80% of its capacity.

In either case, when the battery reaches 80% discharge, its voltage under load begins to fall rapidly, as is shown in Figure 16, and the fall-off rate gets steeper and steeper as the 100% discharge point is approached.

From Figure 16 you can see that the voltage under load  when measured at a constant current - is highly predictable. Any change in voltage is determined by the number of ampere-hours drawn from the battery. Thus, the change in voltage under load is a measure of the charge withdrawn and, therefore, of the capacity remaining.

Of course, there are other factors to be taken into account. The first among these is that any measurement of battery characteristics is highly dependent on electrolyte temperature. The higher the temperature the greater the battery capacity, as shown in Figure 13.



Figure 14: How Stabilized Open Circuit Voltage Reflects Stabilized SG


Figure 15: Variation of Open Circuit Voltages as Cell Recovers After Load


The second factor is that our test measurement was made with a constant load, which does not reflect the real world at all. In fact, we know that interrupting or reducing the load long enough to allow some "recovery" actually increases the remaining capacity. Also an increase in the load reduces the amount of remaining capacity.

In either case, the measured voltage under load changes as the conditions change. If electrolyte temperature increases, so does voltage under load; if the load is interrupted and the battery "recovers," the measured voltage increases, and so on. There is no way to tell from the measured voltage what caused the change, but the voltage under load always decreases as capacity is withdrawn from the battery.

Ampere-hour Measurements

An ampere-hour meter integrates current in amperes with time in hours. Displaying ampere-hours of consumption, it can be used to indicate state-of-charge. Given the rated capacity of a battery, the state-of-charge can be calculated by subtracting ampere-hours consumed from rated capacity. This can be done by the Ah instrument and displayed directly as state-of-charge.


Figure 16: Cell Voltage at Two Constant Currents