## 16 November 2010

### OTTV: what it is and how to calculate it

PAUL HAY Capital Projects

# Overall Thermal Transmission Value (OTTV)

Author:            Paul Hay
e-mail:              paul.hay@phcjam.com

## 1.0  WHAT IS OTTV?

1.1            Overall Thermal Transmission Value (OTTV) is the measure of external heat-gain transmitted through a unit area of a building’s wall or roof;

1.2       OTTV is recorded in units of W/m2.

1.3       OTTV concerns conductive & radiative heat-gains transmitted through glazing and opaque components.

2.0  OTTV VARIABLES

2.1       Equivalent Temperature Differential (TDeq) is the theoretical difference between outdoor and indoor temperatures that would result in a heat transfer equivalent to the effects of solar heat-gains, thermal storage and actual temperature difference on an opaque component, as a roof [unit = K];

2.2       Solar Factor (SF) is the average hourly value of solar insolation [unit = W/m2];
2.2.1.  EEBC-94 states that SF = 435 W/m2 for roofs; and
2.2.2.  SF = 372 W/m2 for walls.

2.3       Shading Coefficient (SC) is the ratio of solar heat-gain through any fenestration compared to that through an unshaded, 3-mm thick double-strength glass.

SC =   Solar Heat-Gain through any fenestration                                              [2.1]
Solar Heat-Gain through reference glass

3.0  CALCULATING OTTV OF ROOFS

3.1       EEBC-94 specifies the maximum OTTV for roofs as 20 W/m2 ;

3.2       There are two equations for calculating OTTVs for roofs.
3.2.1   For roofs without skylights,

OTTVr =          [DT x Ur] + [(TDeq - DT) x Ac x Ur]                                                    [3.1]

where,
OTTVr = Overall Thermal Transmission Value of a roof, W/m2
DT       = Temperature Difference, K
= Td - Ti
Td        = Design Temperature, C
= 33.9 C, for Kingston

Ti         = Thermostat set-point, C
TDeq    =  Equivalent Temperature Differential, K
Ac        = Solar absorptance (0<Ac<1)
Ur        = Overall Thermal Transmission Coefficient of roof, W/m-K

 Fig. 1:  Shading Coefficients for Fenestration

3.2.2   For roofs with skylights,

OTTVr =          [DT x Ur x (1-SRR)] + [(TDeq - DT) x Ac x Ur x (1-SRR)] +
[DT x Us x SRR] + [SF x SCs x SRR]                                             [3.2]
where,
SRR   = Skylight-to-Roof Ratio (0<SRR<1)
SF       = Solar Factor for roof, W/m2
SCs     = Shading Coefficient of skylights (0<SCs <1)
Us        =  Overall Thermal Transmission Coefficient of roof, W/m-K

4.0  CALCULATING OTTV OF WALLS

4.1       EEBC-94 species the maximum OTTV for walls as (a) 67.7 W/m2 for large offices [Area > 3,700 m2] (b) 61.7 W/m2, for smaller offices and (c) 53.1 W/m2 for other buildings;

4.2       OTTVi for a wall is calculated as follows:

OTTVi =          [DT x Ui x (1-WWRi)] + [(TDeq - DT) x CFi x Ac x Ui x (1-WWRi)] +
[DT x Uf x WWRi] + [SF x CFi x SCi x WWRi]                               [4.1]
where,
OTTVi = Overall Thermal Transmission Value of a wall “i”, W/m2
Ui         =  Overall Thermal Transmission Coefficient of wall “i”, W/m-K
WWRi = Window-to-Wall Ratio for wall “i” (0<WWRi<1)
SF       = Solar Factor for wall, W/m2
CFi      = Correction Factor for orientation of wall “i”
SCi      = Shading Coefficient of fenestration on wall “i” (0<SCi <1)
Uf        =  Overall Thermal Transmission Coefficient of fenestration, W/m-K

4.3       Overall OTTV for walls is calculated as follows:

OTTVw =         [(A1 x OTTV1 ) + (A2 x OTTV2) +.........+ (Ai  x OTTVi )]                  [4.2]
(A1 + A2 + ..............+ Ai)
where,
OTTVw = Overall OTTV for walls “1" to “i”
Ai         =   Area of wall “i”

## 5.0  SAMPLE OTTV CALCULATIONS

Calculate the OTTV for an office building constructed as follows:

Location:        Kingston, Jamaica                               Tin                = 24.4 deg.C
Dimensions:    18 m x 18 m x 3.6 m high                    Orientation    = North
Ac(r)               = 0.35                                                 TDeq(r)         = 23.0 deg.C
Ac(w)              = 0.70                                                 TDeq(w)          = 23.0 deg.C
SRR               = 0.01                                                 Ur                 = 1.10 W/m2-K
WWR            = 0.33                                                 Us                 = 5.40 W/m2-K
SCs                = 0.50                                                 Uw                = 3.01 W/m2-K
SCs                = 0.50                                                 Uf                 = 4.60 W/m2-K

DT       = Td - Tin
Where,
Td        = Design temperature         = 33.9 deg.C, for Kingston

ˆ          DT       = 33.9 - 24.4  = 9.5 K

(A)         For a roof with skylights,

OTTVr =          [DT x Ur x (1-SRR)] + [(TDeq(r) - DT) x Ac(r) x Ur x (1-SRR)] +
[DT x Us x SRR] + [SF(r) x SCs x SRR]                                          [5.1]
where,
SF(r)     = Solar Factor for roof         = 435 W/m2, for Jamaica

ˆ          OTTVr =          [9.5 x 1.10 x (1- 0.01)] + [(23.0 - 9.5) x 0.35 x 1.10 x (1- 0.01)] +
[9.5 x 5.4 x 0.01] + [435 x 0.5 x 0.01]
=          10.35 + 5.15 + 0.51 + 2.18
=          18.2 W/m2

(B)         OTTVi for a wall is as follows:

OTTVi =          [DT x Ui x (1-WWRi)] + [(TDeq(w) - DT) x CFi x Ac(w) x Ui x (1-WWRi)] +
[DT x Uf x WWRi] + [SF(w) x CFi x SCi x WWRi]                            [5.2]
where,
SF(w)    = Solar Factor for wall         = 372 W/m2, for Jamaica
CFi      = Correction Factor for orientation of wall “i”
CF1     = 0.96, for east wall

ˆ          OTTV1 =         [9.5 x 3.01 x (1 - 0.33)] + [(23.0 - 9.5) x 0.96 x 0.7 x 3.01 x (1 - 0.33) +
[9.5 x 4.60 x 0.33] + [372 x 0.96 x 0.5 x 0.33]
=          19.16 + 18.30 + 14.42 + 58.92
=          110.8 W/m2

Similarly, CF2           =          1.09, for south wall

ˆ          OTTV2 =         19.16 + 20.77 + 14.42 + 66.90       =          121.3 W/m2

CF3     =          1.36, for west wall

ˆ          OTTV3 =         19.16 + 25.92 + 14.42 + 83.48       =          143.0 W/m2

CF4     =          0.58, for north wall

ˆ          OTTV4 =         19.16 + 11.05 + 14.42 + 35.60       =          80.2 W/m2

(C)         Overall OTTV for walls is as follows:

OTTVw =         [(A1 x OTTV1 ) + (A2 x OTTV2) +.........+ (Ai  x OTTVi )]                  [5.3]
(A1 + A2 + ..............+ Ai)
Where,
A1          =  A2    =  A3    =  A4    = 18 x 3.6       = 64.8 m2

ˆ          OTTVw =         [(64.8 x 110.8) + (64.8 x 121.3) + (64.8 x 143.0) + (64.8 x 80.2)]
(64.8 + 64.8 + 64.8+ 64.8)
=          113.8 W/m2