Chiller Sizing for an Ice Arena
1. Introduction
Ice arenas are among the most energy-intensive objects of sports infrastructure. A significant part of the operating costs of such facilities is determined by the operation of the refrigeration system that ensures the creation and maintenance of the required temperature of the ice surface under changing external and internal influences. Unlike most public buildings, in ice arenas there are simultaneously coexisting zones with sharply different temperature levels: the ice surface with a temperature of about -4 … -8 °C, the volume of air above the ice with a temperature of about 8 … 15 °C and, in the case of indoor arenas, spectator areas designed for near-comfortable conditions. This combination leads to a complex structure of heat fluxes and increased requirements for the accuracy of the cooling load calculation.
The cooling machine (chiller) is the central element of the arena refrigeration system. The composition and distribution of heat fluxes differ markedly between indoor and outdoor arenas. In indoor arenas, radiant heat transfer between the ice surface and the surrounding enclosures, convection with moist air under the roof, heat fluxes from artificial lighting and intermittent loading from the pouring of ice dominate. In outdoor arenas, solar radiation, convective heat transfer with outdoor air and wind effects are key, while the roof structure and internal enclosures are not.
From an engineering point of view, the chiller calculation for an ice arena comes down to determining the total specific heat flux on the ice surface and recalculating it into the required cooling capacity, taking into account the operating margin. It is necessary to take into account the radiant, convective, condensation, conduction and operational components of heat fluxes. Their contribution depends on the geometry of the venue, type of arena (indoor or outdoor), air parameters, design of enclosures, presence or absence of screens under the roof, as well as on the operating mode (training mode, mass skating, competitions with full seating).
Practice shows that the use of simplified enlarged specific loads without analysing the structure of heat inflows leads either to overestimation of the installed cooling capacity of the chiller and increase in capital costs, or to insufficient capacity of the installation and inability to maintain the required ice temperature in the calculated conditions. Therefore, professional design requires a methodology that relies on physically based dependencies and allows to obtain the design load with controlled accuracy based on the initial parameters of the arena, climatic data and specified operating conditions.
This paper discusses a consistent approach to calculating the chiller cooling load for ice arenas of standard size 30×60 m, suitable for implementation as an engineering calculation.
For a preliminary calculation of an ice arena you can use our online calculator, or contact our technical specialists for a more detailed calculation for your application.
Fig 1. –Online calculator for calculating the heat load of an ice arena
2. Physical mechanisms of heat fluxes
2.1. ice slab structure as an element of heat transfer
A typical slab design consists of the following layers: a 25-35 mm thick ice layer, a concrete cooled slab with pipes for coolant circulation, a thermal insulation layer, a heated slab and a base of compacted soil. Each layer has its own thermal conductivity, and the total heat transfer resistance determines the conductive flux from the ground to the ice surface. In the presence of insulation and ground heating, this component is relatively small (5-10 W/m²), but should be taken into account for annually operated arenas, especially in the off-season. In stable operation, the ground temperature is maintained above zero, preventing frost heaving.
Fig. 2 – Typical ice arena field design
2.2 – Radiant heat transfer between ice and envelope structures
In indoor arenas, radiant heat transfer is the dominant source of heat gain. The ice surface has a high degree of blackness (0.96-0.98) in the infrared range in which the ceiling and walls radiate. The flux density is determined by the fourth degree of the absolute temperature of the enclosures. At air temperatures of 10…15 °C and ice temperatures of -4…-6 °C, the radiant flux reaches 70-100 W/m². A characteristic property is a strong dependence on the roof material: galvanised steel provides a 1.8-fold reduction of the flux, metallised screens – 3 or more times. The radiant component determines the total load to a greater extent than any other processes.
Fig. 3 – Radiant heat flux from unshielded envelopes reduced to the ice surface
2.3 – Convective heat exchange with the air environment
The convective component arises from the temperature difference between the air above the ice surface and the ice itself. For calm air, the heat transfer coefficient α is 2-4 W/(m²-K), while for weak circulation it is 4-6 W/(m²-K). The final flux q_k = α-(t_v – t_l) is typically 40-70 W/m² for closed arenas. Improperly organised air supply to the ice surface results in a doubling of the convective load. In open arenas, convection is the second most important source due to wind effects increasing α to 8-12 W/(m²-K).
2.4. humidity processes and water vapour condensation
At relative humidity above 60-65 % condensation on the ice surface is possible. This process causes the release of latent heat of vapour formation, increasing the heat load by 2-5 W/m². Although the contribution of condensation is relatively small, it is critical in facilities where high humidity is generated by the presence of spectators and recirculation ventilation. In addition, condensation on enclosures reduces their radiant temperature, indirectly altering radiant exchange.
2.5. heat conduction through the slab structure and the ground
The conductive component is determined by the temperature gradient between the ground (or heated slab) and the ice surface. With insulation and underfloor heating, the flux q_pl is typically 5-10 W/m². In structures without ground heating or in conditions of low base temperature, this load increases and becomes significant. The conductive component is stable in time and does not depend on the arena operation mode.
2.6. heat flux from lighting
Lighting fixtures used in sports arenas emit heat, part of which falls on the ice surface. The absorbed fraction is determined by the spectrum of the light source and the angle of illumination, typically being 3-7 W/m² for metal halide lamps and 2-4 W/m² for LED systems. Even when relatively small, this component is constant and is part of the total heat balance.
2.7. Operating loads: ice recovery and human error
Hot water ice recovery is one of the most energy intensive operational processes. A water layer less than a millimetre thick at a temperature of 30-50 °C generates tens of kilowatt hours of heat, which is equivalent to a significant increase in the current refrigeration load. Only part of the fill heat is immediately removed by the chiller and the remainder is stored in the ice mass, causing a temporary increase in its temperature. If the system does not have sufficient reserve capacity, the ice has time to warm up to a critical level and the chiller is forced to switch to multiple compressor operation or approach its capacity limit.
The load from people on the ice is relatively small (less than 2 %), but indirectly affects the frequency of pours by destroying the top ice layer.
2.8. cumulative effect of heat fluxes
The combination of the above factors forms the total heat flux q_Σ, which determines the required cooling capacity of the chiller. For closed arenas, radiant and convective fluxes dominate, while for open arenas, solar radiation and convection dominate. An understanding of the heat flux pattern is necessary for the subsequent calculation presented in the third section.
Figure 4 – Structure of heat loads for enclosed ice arenas described in ASHRAE 2010
3. Methodology for calculating the heat load of an ice arena (indoor and outdoor)
The calculation methodology includes two independent blocks:
- Start-up (starting) load calculation – determines the power required for initial ice freezing and cooling of the structure arrays.
- Operating load calculation – determines the chiller capacity required to maintain the ice temperature with all heat inflows.
Typically, the capacity of the chiller is selected based on the operating load, while the starting load calculation is used to select the time of start-up and estimate the load on the system during the start-up period.
3.1: General structure of the heat balance
The total heat flux density entering the ice surface is determined by the expression:
q_Σ = q_radiation q_k q_condensation q_pl q_osv q_exp
where
q_beam – radiant component;
q_k – convective component;
q_condens – flux of latent heat of condensation;
q_pl – heat transfer through the slab and ground;
q_osv – heat load from lighting devices;
q_exp – operational loads (primarily ice recovery).
Chiller cooling capacity:
Q_chill = A – q_Σ – k_zap
where
A is the area of the ice area;
k_zap – reserve coefficient (1.15-1.30 for indoor arenas, 1.30-1.50 for outdoor arenas).
3.2. heat fluxes of a closed ice arena
3.2.1 Radiant heat exchange
Heat flux:
q_radiant = c₀ – ε_pr – (T_ogr⁴ – T_l⁴),
where
c₀ = 5.67-10-⁸ W/(m²-K⁴);
ε_pr – the reduced degree of blackness of the system “ice – fences” (0.85-0.93);
T_ogr, T_l – absolute temperatures of enclosures and ice.
For conditions (t_oð = 12…15 °C, t_l = -4…-6 °C) q_radiation is 70-100 W/m².
When using screens:
- galvanised steel ε ≈ 0.28;
- metallised screens ε ≈ 0.1.
3.2.2 Convective heat exchange
Convection is conveniently calculated through the air velocity w above the ice surface:
α = 3.14 3.55-w (W/(m²-K))
Heat flux:
q_k = α – (t_w – t_l).
Values usually lie in the range 40-70 W/m².
3.2.3 Condensation of water vapour
For engineering evaluation:
q_condensation ≈ 0.7 – (φ/100) – (t_v – t_l),
which gives 1-4 W/m² at φ = 50-65 %.
In conditions of high humidity (competitions with spectators, inefficient ventilation) this may increase.
3.2.4 Heat transfer through the slab
Heat flux:
q_pl = λ_eq – (t_gr – t_l) / δ_eq.
For an insulated slab q_pl = 5-10 W/m².
3.2.5 Heat from lighting
q_osv = (P_osv – η_pogl) / A.
Values usually lie in the range of 3-7 W/m².
Operating load: ice filling
Heat load from pouring:
Q_hall = ρ – A – h – (c_v-Δt r c_l – |t_l|)
Where
h – thickness of the fed layer;
Δt – temperature difference between water and 0 °C;
c_v, c_l – heat capacities of water and ice;
r – heat of freezing.
The load is determined by the time interval between pours.
3.3. Heat fluxes of an open ice arena
3.3.1 Solar radiation
Basic formula for solar heat flux:
q_sol = I_sol – e_l
where
I_sol – total solar radiation on the horizontal surface (200-600 W/m²);
e_l – absorption coefficient of ice in the visible range (0.5-0.7).
It is most critical on clear days with low sun, when the share of direct and scattered radiation is maximum.
3.3.2 Convection
In the case of wind forcing:
α = 3.14 3.55-w,
where w is typically 1-4 m/s , α ranges from 7-17 W/(m²-K).
Heat flux in simplified form:
q_k = α – (t_w – t_l).
3.3.3 Heat conduction and pouring
Estimated in the same way as in closed arenas.
3.3.4 Total heat flux of an open arena
q_Σ,open = q_sol q_k q_pl q_expl
3.4 Calculation of start-up (starting) load
As it was written earlier, the capacity of the refrigeration machine is selected according to the operating load, while the starting load calculation is used to select the start-up time and to estimate the load on the system during the start-up period. Therefore, below we will only list the factors that make up the starting load:
- cooling the water to 0 °C;
- freezing it into ice;
- cooling the ice to operating temperature;
- cooling of the concrete slab;
- cooling of the coolant in the pipes.
4. Example of cooling load calculation for a 30×60 m indoor ice arena
A standard ice arena of 30×60 m is considered. The area of the ice surface:
A = 30 – 60 = 1800 m²
Ice temperature:
t_l = -4 °C
Air temperature at the level of the false ceiling:
t_v = 12 °C
Relative air humidity:
φ = 55 %
Ground (or heated plate) temperature:
t_gr = 6 °C
The reduced degree of blackness of the “ice – enclosures”:
ε_pr = 0.88
Air velocity above the ice surface:
w = 0.25 m/s
Lighting power:
P_osv = 22 kW
Absorption coefficient of radiation by ice:
η_pogle = 0.45
Operational thickness of one pour:
h_zall = 0.6 mm = 0.0006 m
Water temperature for pouring:
t_vz = 50 °C
Reserve factor:
k_zap = 1.25
4.2. calculation of individual heat flows
4.2.1 Radiant heat transfer
Absolute temperatures:
T_ogr = 12 273.15 = 285.15 K
T_l = -4 273.15 = 269.15 K
Radiant heat exchange:
q_radiant = 5.67-10-⁸ – 0.88 – (285.15⁴ – 269.15⁴) ≈ 69.5 W/m²
4.2.2 Convective heat exchange
Heat transfer coefficient:
α = 3.14 3.55-w = 3.14 3.55-0.25 = 4.03 W/(m²-K)
Heat load:
q_k = 4.03 – (12 – (-4)) = 4.03 – 16 = 64.5 W/m²
4.2.3 Condensation load
q_condens = 0.7 – (φ/100) – (t_v – t_l) = 0.7 – 0.55 – 16≈ 6.2 W/m²
4.2.4 Heat conduction through the slab
Let’s use the enlarged value for the construction with insulation:
q_pl = 8 W/m²
4.2.5 Light absorption by ice
Heat flux density:
q_osv = (P_osv – η_pogl) / A = (22000 – 0.45) / 1800≈ 5.5 W/m²
4.2.6 Thermal effect of one pour (average per hour)
Water mass:
m = ρ – A – h = 1000 – 1800 – 0.0006 = 1080 kg
Thermal effect:
Q_hall = m – [ c_v-(t_vz – 0) r c_l-|t_l| ]
Substitution:
c_v = 4200 J/(kg-K)
c_l = 2100 J/(kg-K)
r = 334000 J/kg
Δt = 50 K
Q_hall = 1080 – [4200-50 334000 2100-4] = 5.96-10⁸ J
Conversion to kWh considering the interval between pours of 4 hours:
Q_zal = 5.96-10⁸ / (4 – 3.6-10⁶ ) ≈ 42 kW
Per m²:
q_exp = 42-1000 / 1800 ≈ 23.3 W/m²
4.3. total heat flux density
Summarise all components:
q_Σ =69.5 (radiant) 64.5 (convective) 6.2 (condensation) 8.0 (slab) 5.5 (lighting) 23.3 (fill) = 177 W/m²
4.4. required cooling capacity
Q_chil = A – q_Σ – k_zap = 1800 – 0.177 – 1.2 ≈ 380 kW
Thus, for a closed arena of standard size 30×60 m with the accepted air parameters and operating conditions, the required cooling capacity is:
Q_chiller ≈ 380 kW
5. Example of calculation of refrigeration load for an open ice arena 30×60 m
We consider an open ice rink of 30×60 m, operated in the transitional period at positive outdoor temperatures and the presence of solar radiation. The area of the ice surface:
A = 30 – 60 = 1800 m²
The calculation is performed for daytime operation in conditions close to the most loaded for an outdoor arena.
5.1. initial data
Ice temperature:
t_l = -4 °C
Outdoor air temperature:
t_v = 4 °C
Wind speed over the ice surface:
w = 2.0 m/s
Intensity of solar radiation on the horizontal surface:
I_sol = 400 W/m²
(average level for a cloudy-clear day in the off-season)
Absorption coefficient of solar radiation by ice:
α_l = 0.6
Ground (or warm base plate) temperature:
t_gr = 5 °C
Heat transfer through the slab (enlarged):
q_pl = 8 W/m²
Lighting mode:
artificial lighting is not taken into account (daytime mode, q_osv = 0)
Ice filling:
3 pours for ice recovery per day are accepted, layer
h_hall = 0.6 mm = 0.0006 m
Water temperature for restoration:
t_vz = 45 °C
(colder water is often used for outdoor rinks)
Reserve coefficient:
k_zap = 1.40
5.2. calculation of individual heat flows
5.2.1 Solar radiation
Absorbed flux density:
q_sol = I_sol – α_l = 400 – 0.6 = 240 W/m²
This is the main source of heat fluxes for an outdoor ice rink during daytime.
5.2.2 Convective heat exchange
Heat transfer coefficient:
α = 3.14 3.55-w = 3.14 3.55-2.0 = 10.24 W/(m²-K)
Heat flux:
q_k = α – (t_w – t_l) = 10.24 – (4 – (-4)) = 10.24 – 8 = 81.9 W/m²
5.2.3 Heat conduction through the slab
For an outdoor rink, the same slab design is assumed as for indoor arenas, with insulation and ground heating. Assume:
q_pl = 8 W/m²
5.2.4 Load from ice pouring (similar to item 4.2.6.)
q_exp ≈ 23.3 W/m²
5.3. total heat flux density
Let’s sum up the acting components:
q_Σ,open = q_sol q_k q_pl q_exp = 240 81.9 8 23.3 ≈ 353.2 W/m²
5.4. required cooling capacity of the chiller
Design capacity:
Q_chill = A – q_Σ,open – k_zap =
Q_chil = 1800 – 0.353 – 1.30 ≈ 825 kW
6. Conclusion
The calculation of the cooling load of an ice arena is a multi-component thermal engineering problem in which each physical phenomenon – radiant heat exchange, convection, conduction, solar radiation, moisture condensation and operational processes – contributes to the overall heat balance. The degree of influence of the individual components is determined by the type of arena (closed or open), roof and fence design, air distribution parameters, climatic conditions and operating mode.
For closed arenas with properly organised ventilation and humidity control, the total operating load for a 30×60 m ice arena is in the range of 160-190 W/m².
For open arenas, the dominant factors are solar radiation and convection enhanced by wind effects. In the absence of enclosing surfaces, the value of the radiant flux is determined not by the temperature of the structures, but by the absorption of short-wave solar radiation by ice. At significant insolation, solar flux can provide half or more of the total heat load. Under such conditions, operational loads reach 250-400 W/m² and higher.
The results of calculations show that the use of aggregated specific heat fluxes without analysing the load structure leads to significant errors. A full-fledged engineering methodology should be based on physical models of radiant and convective exchange, take into account operating modes and peculiarities of the slab design. The presented approach allows to quantify the contribution of each heat flux and correctly determine the required chiller cooling capacity for any operating conditions.
When designing real objects, it is recommended to perform the calculation in two modes:
- operational – to select the chiller capacity;
- start-up mode – to estimate the time ofstart-up and the load on the system during the first hours of operation.
An operational capacity reserve should also be provided, depending on the type of arena and operating conditions: 1.15-1.30 for indoor facilities and 1.30-1.50 for outdoor venues. Such values ensure reliable operation of the refrigeration system under changing climatic influences, variations in air parameters, unstable solar radiation fluxes and operational disturbances.
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Author of the article:
Sergey Stafiychuk, Sales Manager
12.12.2025