The room sensible heat factor line can also be drawn on the psychrometric chart without knowing the condition of supply air. The following procedure illustrates how to plot this line, using the calculated RSHF, the room design conditions, the sensible heat factor scale in the upper right hand corner of the psychrometric chart, and the alignment circle at 24°C dry-bulb and 50% relative humidity:

1. Draw a base line through the alignment circle and the calculated RSHF shown on the sensible heat factor scale in the upper right corner of psychrometric chart (1-2),
2. Draw the actual room sensible heat factor line through the room design conditions parallel to the base line in Step 1 (3-4), As shown, this line may be drawn to the saturation line on the psychrometric chart.

The grand sensible heat factor is the ratio of total sensible heat to the grand total heat load that the conditioning plant must handle, including the outdoor heat loads. This ratio is determined from the following equation:

Air passing through the conditioning plant increases or decreases in temperature and/or moisture content. The amount of rise or fall is determined by the total sensible and latent heat loads that the conditioning plant must handle. The condition of the air entering the plant (mixture condition of outdoor and return room air) and the condition of the air leaving the plant may be plotted on the psychrometric chart and connected by a straight line (1-2), This line represents the psychrometric process of the air as it passes through the conditioning plant, and is referred to as the grand sensible heat factor line.

The slope of the GSHF line represents the ratio of sensible and latent heat that the plant must handle. This is illustrated by Δhs (sensible heat) and Δhl (latent heat).

The grand sensible heat factor line can be plotted on the psychrometric chart without knowing the condition of supply air, in much the same manner as the RSHF line. Step 1 (1-2) and Step 2 (3-4) show the procedure, using the calculated GSHF, the mixture condition of air to the plant, the sensible heat factor scale, and the alignment circle on the psychrometric chart. The resulting GSHF line is plotted through the mixture conditions of the air to the plant.

Adjusted Room Sensible, Latent and Total Heat

The terminology of 'adjusted' room sensible heat, 'adjusted' room latent heat and 'adjusted' room total heat is introduced in this method. The description 'effective' has traditionally been used to identify the heat quantities associated with this method for psychrometric calculations. Using this method, the value for dehumidified air quantity is given by the equation:

Air Quantity = Effective Room Sensible Heat / [1.2 x (1 - Bypass factor) (Room temp - App. dewpoint)]

Where: Effective room sensible heat = room sensible heat + supply duct sensible heat + portion of outdoor air bypassed through the apparatus.

This equation is not strictly correct because the by-pass factor should be applied to the GTH line. Manually this can only be done by a trial and error process on the psychrometric chart. With the aid of a computer the exact equation is:

Air Quantity = Adjusted Room Sensible Heat / [1.2 x (Room temp - Leaving apparatus temp)] Where: Adjusted Room Sensible Heat = Room Sensible Heat + Supply Duct Sensible Heat Gains

Required air quantity

The air quantity required to simultaneously offset the room sensible and latent loads and the air quantity required through the plant to handle the total sensible and latent loads may be calculated, using the conditions on their respective RSHF and GSHF lines. For a particular application, when both the RSHF and GSHF ratio lines are plotted on the psychrometric chart, the intersection of the two lines (1) represents the condition of the supply air to the space. It is also the condition of the air leaving the plant.

This neglects fan and duct heat gain, duct leakage losses, etc. In actual practice these heat gains and losses are taken into account in estimating the cooling load. Therefore, the temperature of the air leaving the plant is not necessarily equal to the temperature of the air supplied to the space as indicated.

The figure above illustrates what actually happens when these supplementary loads are considered in plotting the RSHF and GSHF lines.

Point (1) is the condition of air leaving the plant and point (2) is the condition of the supply air to the space. Line (1-2) represents the temperature rise of the air stream resulting from supply fan and heat gain to the supply air duct. Line (3-4) represents the temperature rise of the air stream resulting from heat gain to the return air duct and return air fan.

The air quantity required to satisfy the room load may be calculated from the following equation:

The air quantity required through the conditioning plant to satisfy the total air conditioning load (including the supplementary loads) is calculated from the following equation:

The required air quantity supplied to the space is equal to the air quantity required through the plant, neglecting leakage losses. The above equation contains the term tM which is the mixture condition of air entering the plant. With the exception of an all outdoor air application, the term tM can only be determined by trial and error.

Normally this difference in supply air temperature and the condition of the air leaving the plant (tSA – tLDB) and the temperature rise due to return air duct and return air fan (t4 – tRM) are not more than a few °C. To simplify the discussion on the interrelationship of RSHF and GSHF, the supplementary loads have been neglected in the various discussions, formulae and problems in the remainder of this Section. It is emphasized, however, that these supplementary loads must be recognised when estimating the cooling and heating loads.

The RSHF ratio will be constant (at full load) under a specified set of conditions; however, the GSHF ratio may increase or decrease as the outdoor air quantity and mixture conditions are varied for design purposes. As the GSHF ratio changes, the supply air condition to the space varies along the RSHF line.

The difference in temperature between the room and the air supply to the room determines the air quantity required to satisfy the room sensible and room latent loads. As this temperature difference increases (supplying colder air, since the room conditions are fixed), the required air quantity to the space decreases. This temperature difference can increase up to a limit where the RSHF line crosses the saturation line on the psychrometric chart, assuming, of course, that the available conditioning equipment is able to take the air to 100% saturation. Since this is impossible, the condition of the air normally falls on the RSHF line close to the saturation line. How close to the saturation line depends on the physical operating characteristics and the efficiency of the conditioning equipment.

In determining the required air quantity, when neglecting the supplementary loads, the supply air temperature is assumed to equal the condition of the air leaving the plant (tSA = tLDB). The calculation for the required air quantity still remains a trial-and-error procedure, since the mixture temperature of the air (tM4) entering the plant is dependent on the required air quantity. The same procedure previously described for determining the air quantity is used. Assume a supply air rise and calculate the supply air quantity and the mixture temperature to the conditioning plant. Substitute the supply air quantity and mixture temperature in the equation for determining the air quantity through the plant and calculate the leaving condition of the air from the plant. This temperature must equal the supply air temperature; if it does not, a new supply air rise is assumed and the procedure repeated.

Determining the required air quantity by either method previously described is a tedious process, since it involves a trial-and-error procedure, and in actual practice accounting for the supplementary loads in determining the supply air, mixture and leaving air temperatures.

This procedure has been simplified, by relating all the conditioning loads to the physical performance of the conditioning equipment, and then including this equipment performance in the actual calculation of the load.

This relationship is generally recognised as a psychrometric correlation of loads to equipment performance. The correlation is accomplished by calculation the ‘effective surface temperature’, ‘bypass factor’, and ‘effective sensible heat factor’. These will permit a simplified calculation of supply air quantity.

Bypass factor is a function of the physical and operating characteristics of the conditioning plant and, as such, represents that portion of the air which is considered to pass through the conditioning plant completely unaltered. The physical and operating characteristics affecting the bypass factor are as follows:

1. A decreasing amount of available plant heat transfer surface results in an increase in bypass factor, i.e. less rows of coil, less coil surface, less/wider fins or wider spacing of coil tubes.
2. A decrease in the velocity of ait through the conditioning plant results in a decrease in bypass factor, i.e. more time for the air to contact the heat transfer surfaces.

Decreasing or increasing the amount of heat transfer surface has a greater effect on bypass factor than varying the velocity of air through the plant.

There is a psychrometric relationship of bypass factor to GSHF and RSHF. Under specified room conditions, outdoor design conditions and quantity of outdoor air, RSHF and GSHF are fixed. The position of RSHF is also fixed, but the relative position of GSHF may vary as the supply air quantity and supply air condition change.

To properly maintain room design conditions the air must be supplied to the space at some point along the RSHF line. Therefore, as the bypass factor varies, the relative position of GSHF to RSHF changes, as shown by the dotted line. As the position of GSHF changes, the entering and leaving air conditions at the plant, the required air quantity, bypass factor and the apparatus dewpoint also change.

The effect of varying the bypass factor on the conditioning equipment is as follows:

1. Small bypass factor –

(a) Higher ADP – DX equipment selected for higher refrigerant temperature and chilled water equipment would be selected for less or higher temperature chilled water. Possibly smaller refrigeration machine.

(b) Less air – smaller fan and fan motor.

(c) More heat transfer surface – more rows of coil or more coil surface available.

(d) Smaller piping if less chilled water is used.

1. Larger bypass factor –

(a) Lower ADP – Lower refrigerant temperature to select DX equipment, and more water or lower temperature for chilled water equipment. Possibly larger refrigeration machine.

(b) More air – larger fan and fan motor.

(c) Less heat transfer surface – less rows of coil or less coil surface available.

(d) Larger piping if more chilled water is used.

As previously indicated, the entering and leaving air conditions at the conditioning plant and the apparatus dewpoint are related psychrometrically to the bypass factor. Although it is recognised that bypass factor is not a true straight line function, it can be accurately evaluated mathematically from the following equations: &

Note: The quantity (1 – BF) is frequently called contact factor and is that portion of the air leaving the plant at the ADP.