The "thermal efficiency" we find in sales literature, therefore, is the measure of a boiler's energy efficiency at a welldefined set of operating conditions; namely, at steady state and at full firing rate. When the boiler is operating at those set test conditions, thermal efficiency is an accurate measure of energy efficiency. Unfortunately, thermal efficiency does not account for performance at any other operating condition or rate of fire. A much more useful measure of energy efficiency, one that considers operating conditions, is "dynamic efficiency."
Dynamic Efficiency
Dynamic efficiency provides a much more accurate indication of energy efficiency as it accounts for the varying nature of the heating load. Specifically, dynamic efficiency is the ratio of useful output to total input at a specific load condition. Dynamic efficiency includes the effects of standby losses, and the variation of steady state thermal efficiency vs. firing rate. With exception of onsite seasonal efficiency metering, dynamic efficiency provides the single most accurate method of determining the energy efficiency of a system. We shall now consider, in turn, how dynamic efficiency is affected by the various firing configurations currently in use, the effects of firing rate on thermal efficiency, and the impact of standby losses.
Firing Configurations
There are four widely used operating configurations for gas fired appliances: modulating fire, onoff, hilow, and multistage firing. Modulating fire is accomplished by mechanically varying the size of the gas admittance opening of one or more special "modulating" gas valves. With the gas valve completely open the boiler fires at it's full fire rate. The unit is said to be at "full turndown" when it fires at it's lowest firing rate. The "turndown ratio" is the ratio of full fire rate to full turndown firing rate and is a function of boiler design. A turn down ratio of 5:1 would indicate that a boiler is capable of a full turndown firing rate of 20% (5:1 ( 100% fire : 20% fire).
Onoff, hilow and multistage firing configurations are accomplished by opening or shutting one or more staged gas valves. Onoff, or one stage boilers, usually employ a single gas valve that is either fully open or fully shut. Hilow, or twostage boilers and multistage boilers typically utilize several one stage or two stage valves to provide an appropriate number of firing increments. For example, a typical four stage boiler might use two twostage valves giving it four incremental firing rates; 100% fire, 75%, 50%, and 25% of full firing rate.
Thermal Efficiency at Less than Full Fire
Most boilers are designed to achieve maximum thermal efficiency at full fire rate. As firing rate decreases, less gas is burned which reduces the amount of hot combustion gases generated at the burner. This in turn affects a number of combustion related factors including excess air ratio, combustion gas to heat exchanger surface ratio, the flow characteristics of the combustion gases, and vent dynamic pressure. The combination of effects caused by the reduction of firing rate on boiler performance is complex, the details of which are beyond the scope of the current discussion. Suffice it to say that reducing the firing rate will impact the firing characteristics of the boiler, including thermal efficiency.
The net effect of firing rate on thermal efficiency is primarily determined by boiler design. In general, for most boiler types, thermal efficiency will decrease as the firing rate decreases. In atmospheric draft boilers, the reduction in the volume of hot combustion gases at lower fire rates results in a lower differential pressure through the vent system. This is due to the reduced buoyancy, or thermal driving head, of the less voluminous flue gases. The reduced differential pressure leads to a small reduction in the volume of excess air entrained in the combustion gases. Since this change is small in comparison to the change in the volume of combustion gases, the excess air ratio actually increases. Higher excess air ratios result in lower temperature gases flowing through the heat exchanger. The lower differential temperature between the gases and the heating fluid, in turn, leads to a less efficient transfer of heat, which lowers the thermal efficiency of the boiler. Graph 1 demonstrates the resultant change in thermal efficiency in a typical modulating atmospheric boiler.
As can be seen above, a properly designed boiler can generate fairly consistent thermal efficiencies at various firing rates. In this example, A Raypak H6824 loses less than four percent thermal efficiency over its entire firing range. Parenthetically, in an outdoor reset system, where system temperature decreases with lowering heating load requirements, a properly designed boiler will exhibit an even smaller decrease in thermal efficiency. A typical Raypak modulating boiler equipped with an outdoor reset control will lose less than 2% thermal efficiency across its full range of fire. Unless the heat exchanger area and excess air ratio are exactly varied to match the firing rate (an expensive and complicated proposition), all boilers will exhibit similar characteristics. Examples of the thermal efficiency at various firing rates for other configurations of boilers are given in Table 1.
Table 1. Thermal Efficiencies at Various Rates of Fire
Configuration 
Firing Mode 
Firing Rate 
Thermal Efficiency 
OnOff 
On 
100% 
82% 
Two Stage 
High Fire 
100% 
82% 

Low Fire 
50% 
79.5% 
Four Stage 
High Fire 
100% 
82% 

Third Stage 
75% 
81% 

Second Stage 
50% 
79.5% 

Low Fire 
25% 
78% 
Standby Losses
Standby losses account for thermal energy lost from the boiler while the equipment is in a nonfiring or standby mode. Although this energy may provide heat for the mechanical room in indoor installations, it is otherwise lost from the system. The amount of standby loss is primarily dependent upon three factors; system to ambient differential temperature, boiler design, and boiler operating practices.
When the boiler is not firing, to a greater or lesser extent, it becomes a radiator. Thermal energy stored in the heating medium migrates to areas of lower temperature, namely the air moving through and around the heat exchanger. The greater the temperature difference between the ambient air and the heating medium, the more heat will be lost. Standby losses, therefore, vary proportionally with the temperature differential between the ambient air and system temperature.
Several methods are used to reduce standby losses by lowering the temperature differential including: lowering the system operating temperature, turning off the boiler circulating pump, and reducing the air flow through the heat exchanger while in standby. While all three methods are valuable, the first two options, which are more operating method than design dependent, are by far the most effective. The third option, restricting air flow, which is design dependent, is measurably less effective due to the impracticality of completely sealing off the combustion chamber while the boiler is in standby. As long as some air flow is present, the boiler will still lose a significant amount of heat convectively.
Incidentally, although a power burner will generally experience lower standby losses than an atmospheric burner, the net effect is not as significant as often touted. In fact, a short cycling power burner will have standby losses three to four times higher than a comparable atmospheric burner. This is due to pre and postfire air purge requirements that result in the power burner fan continuously blowing air across the heat exchanger. Table 2 lists the typical standby losses of various copper finned tube boiler types when used in a large hydronic heating system and when not subject to short cycling.
Table 2. Typical Standby Losses (Percent of Boiler Input Lost per Hour)

System 
Temperature 

140°F 
180°F 
Atmospheric Draft 
w/ Intermittent pump 
1.3% 
2.1% 
w/ Continuous pump 
7.2% 
11.5% 
Power Burner 
w/ Intermittent pump 
1.1% 
1.9% 
w/ Continuous pump 
6.4% 
10.3% 
Note: Ambient temperature assumed to be 70(F. 
The Impact of Standby Losses on Dynamic Efficiency
While the most convenient method of determining dynamic efficiency is on the test stand, the slightly more labor intensive mathematical method we will use here more effectively demonstrates the impact of standby losses and provides verifiable repeatability without extensive laboratory work.
As mentioned earlier, dynamic efficiency is the ratio of useful output to total input at a specific load or firing rate. (See Equation 1.)
Since standby losses directly reduce the useful output of the boiler, they are accounted for by the term, (where represents thermal efficiency.)
A lightly loaded boiler with an output demand less than its lowest fire rate will necessarily spend some portion of time in standby, and will therefore have some standby losses. The amount of standby loss is determined by both the percentage of time spent in standby and the standby loss percentage Similarly, boiler input is dependent upon the percentage of time the boiler fires . Since dynamic efficiency is dependent on firing rate, it is appropriate to identify all rate dependent functions (r), transforming Equation 2 into Equation 3.
Simple substitution of Equation 3 into Equation 1, develops a usable equation for mathematically estimating dynamic efficiency:
To illustrate the application of Equation 4, consider two gas fired boilers installed in otherwise identical hydronic heating systems. Boiler A utilizes modulation, Boiler B is limited to onoff fire. Both boilers are rated at 1 MM BTUH input at full fire. The system heating load is currently 250 M BTUH and standby losses are assumed to be 2.5%. In order to generate 250,000 BTUH of usable output, modulating Boiler A will fire continuously at 31.6% fire with a thermal efficiency of 79% (1,000,000 x 31.6% x 79% = 250,000 BTUH). Since Boiler A is firing continuously, it will not have any standby losses. Therefore the dynamic efficiency of Boiler A at 31.6% fire equals the thermal efficiency, or 79%.
Repeating the calculation over the entire range of fire will generate Graph 2.
The onoff boiler, Boiler B, will meet the heat demand by cycling on and off. When Boiler B is firing, it will fire at full fire rate with a thermal efficiency of 82%. To generate 250,000 BTUH per hour of input, Boiler B will have to fire for a total of 18.3 minutes per hour, or 30.5% of the time. (1,000,000 x 100% x 82% x 30.5% = 250,000 BTUH). For 41.7 minutes of the hour (69.5%) the boiler will be in standby, and will be subject to standby losses. The dynamic efficiency of Boiler B load at 30.5% of full fire rate is:
Note: in order to keep the math relatively simple, we have purposely disregarded the extra fire time required to make up standby losses. Compensating would necessitate the use of differential equations to resolve the circular nature of the makeup function. The algebraic method we use is accurate to within +/ 0.5%.
By repeating this calculation across the entire range of heating loads for Boiler B, we develop the dynamic efficiency performance curve of Graph 3.
Note, the curve generated in Graph 3 closely corresponds to data published by the National Bureau of Standards based on tests conducted at the Brookhaven National Laboratory, thus validating our mathematical model.
Analysis of the dynamic efficiency of two stage and four stage boilers generate similar curves. The primary difference between the stage firing curves is the point at which standby losses begin to effect dynamic efficiency. As a rule, regardless of firing configuration, a properly sized hydronic boiler will suffer dynamic efficiency degradation due to standby losses when operated at a load that is below the lowest firing rate. At heat loads lower than the lowest firing rate, dynamic efficiency degradation becomes much more pronounced due to the fractionally greater impact of standby losses. It therefore behooves the user to obtain the best energy efficiency by finding the optimum balance between low turn down and dynamic efficiency.
The dynamic efficiency advantage of modulation is graphical shown below in Graph 4 which compares the dynamic efficiency of modulation to each of the other three firing configurations.
As shown, the primary energy efficiency advantage of modulation occurs at the low fire rates associated with light heating loads. It is appropriate to point out that a properly sized boiler system rarely operates at its design load. Typically a boiler system operates at less than 40% firing rate more than 60% of the time. Furthermore, if the boiler is even moderately oversized, the percentage of time the boiler spends at low fire will increase exponentially.
Accurate Load Tracking
Another advantage of modulation is the ability of a modulating boiler to respond proportionally to rapidly varying load conditions. Whereas a multistage boiler must jump between firing rates, a modulating boiler can exactly match output requirements by minutely adjusting its firing rate. The ability to accurately track load is invaluable in instantaneous and semiinstantaneous systems that require precise temperature control. Indeed, modulation is almost universally specified on temperature critical applications since its superior load tracking accuracy holds system temperatures despite wildly varying load conditions.
In less critical applications, the load tracking ability of modulation is still highly desirable because it reduces the energy waste of over and undershoot. Overshoot occurs when a boiler adds more energy to a system than is immediately required. A common occurrence in staged fire applications, overshoot results in excess energy production which contributes to higher standby losses. Indeed, extreme cases of overshoot at low load conditions can result in short cycling and premature boiler failure.
Undershoot occurs when a boiler fails to add sufficient energy to the system during a firing cycle and is forced to relight to make up the difference. By repeatedly turning on and off, boiler performance degrades due to the cumulative effects of startup losses. As illustrated in Graph 5, short and frequent firing cycles can severely reduce system efficiency.
Note: Graph 5 derived from National Bureau of Standards test data.
As shown above, the optimum firing response is a single continuous burn exactly matched to the output demands of the heat load  a capability only realized with modulation.
Conclusion
Modulating fire has been used for many years by professional engineers and contractors as a safe and effective means to improve system efficiency. By far the best firing configuration available for hydronic heating systems, modulation is also the system of choice for domestic hot water and process loads where the heating load varies widely. Modulation saves money by improving dynamic efficiency during periods of light loads. Modulation provides accurate load tracking and precise temperature control, while minimizing energy waste. Coupled with an advanced control system with anticipatory logic, modulation is, handsdown, the most energy efficient firing configuration currently available.