BACKGROUND OF THE INVENTION 
     It is known that properly twisting a blade of a turbomachine rotor such as a compressor, turbine, fan, pump, etc., improved performance and efficiency can be obtained. However, optimizing a blade section design has generally required extensive aerodynamic test data from wind tunnel and engineering design time. The manufacturing cost of a so-designed sheet-metal fan thereof has generally been prohibitive, particularly in automotive applications. The current energy shortages and noise regulations have led the automotive industry and other sheet metal fan users to consider more efficient and often more expensive fans which consume less energy and generate less noise. 
     SUMMARY OF THE INVENTION 
     This invention is directed to a twisted type sheet-metal fan of relatively simple geometry and of relatively low manufacturing cost to provide an aerodynamically optimized fan having particular utility in automotive cooling fan applications at a competitive cost level. 
     More particularly, the invention may be defined as a sheet-metal fan blade of improved performance and efficiency wherein the camber angle θ and the chord angle γ are so varied along radial positions of the blade that the angles of attack along at least 70% of the radial length of the blade is not less than 2° more than 10° and preferably between 3° and 8° whereby the energy input to the fan blade at any radial position is equal to K H  (r n ) wherein n is between 1 and 2. 
    
    
     IN THE DRAWINGS 
     FIG. 1 is a fragmentary front view of a typical automotive cooling fan of sheet metal constructed according to the teachings of this invention; 
     FIG. 2 is a cross-sectional view of a plurality of adjacent fan blade sections taken along line 2--2 of FIG. 1 at a typical radial station r; 
     FIG. 3a is a front view of a fan blade of the type shown in FIG. 1 wherein an exponent n approximately equals to 2; 
     FIG. 3b is an end view of the blade shown in FIG. 3a; 
     FIG. 4a is a view similar to FIG. 3a but of a conventional automotive cooling fan blade; 
     FIG. 4b is an end view of the blade shown in FIG. 4a; 
     FIG. 5 illustrates test comparison of the efficiencies of the fans illustrated in FIGS. 3a and 3b and 4a and 4b; 
     FIG. 6 shows the improvement of overall fan efficiency as a function of the number of radial stations optimized according to the teachings of this invention. 
     FIG. 7 illustrates a typical set of curves for the indicated test conditions which are experimentally determined by known techniques, from two-dimensional wind tunnel testing of circular, cambered sheet metal plates. As the indicated test conditions vary, an entirely new set of curves will, in general, be generated. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A fan is a device for transferring energy to air. Energy must be transferred to each air particle in front of the fan to cause this particle to move to the rear of the fan. The fundamental equation, known as Euler&#39;s equation, which governs the energy transferred to an air stream across a moving blade section can be written as: ##EQU1## An overall energy balance through the annular flow passage of a typical fan in an incompressible flow field can be written as: ##EQU2## Where: ρ = Density of air 
     r i  = Fan blade inner radius 
     r o  = Fan blade outer radius 
     Δp = Average pressure rise across the fan, i.e., from in front of the fan to the rear of the fan. 
     η oa  = Overall fan efficiency 
     V 1  = Average axial air velocity at fan inlet 
     g = Gravitational acceleration 
     It has been found from extensive tests that fans designed using the following equation provide the best engine radiator cooling performance: (from equations (1) and (2)) 
     
         ΔH.sub.TH = K.sub.H (r.sup.n)                        (3) 
    
     Where: n = a design constant greater than 1 but less than 2. ##EQU3## 
     EXAMPLE 
     The following design example is given to demonstrate the construction and also the manner of making the fan blade of this invention. 
     The design calculations were done by a computer in view of the numerous iterations and large aerodynamic data bank involved and the following presents only the results of the final iteration. The example is done for the fan 10 of FIG. 1 having six blades 12, a combined hub and spider 14 and an overall fan efficiency (η oa ) of 45%. This example is for a fan designed to meet the following conditions: 
     r o  = 14 inches 
     r i  = 4.66 inches 
     R f  = 18 inches 
     ρg = 0.075 lb m  /ft 3   
     Q = 10,000 ft 3  /min. 
     N = Speed of rotation = 2,100 rpm 
     Δp = 3.5 inches of water = 18.2 lb f  /ft 2   
     The exponent n in equation (3) was chosen to be 1.7. Therefore, substituting into equation (4), ##EQU4## These values hold for all radial stations of each blade 12. For a typical blade section, for example, at r = 9.86 inches, (see FIG. 1), the detailed aerodynamic calculations are as follows: ##EQU5## 
     The reader will note that these last three values are vectorially (by trigonometry) determined from FIG. 2. 
     Across a rotating blade row, such as the row of FIG. 2, 
     
         (static pressure rise) = η.sub.R x (reduction of relative dynamic pressure) 
    
     Where η R  = channel efficiency of a rotating blade passage. The known aerodynamic &#34;blade loading&#34; equation is ##EQU6## where C D  = blade drag coefficient. 
     The term σC D  cot φ r  in equation (5) can be rewritten as: ##EQU7## 
     It is known that for sheet-metal fan blades an optimum value for η R  in equation (6) would be 0.8. 
     Now, substituting numerical values into equation (6), ##EQU8## The iteration process starts from here to select a blade cross-sectional configuration at the chosen radial station (r=9.86 in.) which will satisfy C L  σ = 1.013. Firstly, a trial value of C greater than zero is selected, and calculations are made to obtain θ, σ and a/C. Next, FIG. 7 is employed to obtain C L , and then C L  σ is calculated. These four variables are repeatedly calculated until the value of C L  σ obtained by equation (6) is equal to the value of C L  σ obtained by the use of test data such as that shown at FIG. 7. The final iteration results are as follows: 
     C (the chord length, see FIG. 2) was found to be 10.33 inches and all of the remaining geometrical parameters of a circular cambered plate blade can be calculated as follows: ##EQU9## Since (C L ) at α optimum  = C L  σ/σ = 1.013, the selection of a desired geometry is complete. The blade chord angle γ = φ r  + α = 17.82° + 4° = 21.82° 
     Calculations, similar to the above calculations for a radial station r = 9.86 inches, were carried out at various radial stations over at least 70% of the blade length. The final fan geometry is tabulated and compared with the geometry of a conventional fan as follows: 
     
         ______________________________________ 1. OVERALL PERFORMANCE AND DESIGNCONDITIONS:    Fan Designed    Using New Method                 Conventional Fan______________________________________Q, CFM     10,000         10,000N, RPM     2,100          2,100Δp, in. H.sub.2 O      3.5            3.5r.sub.o, in.      14             14r.sub.i, in.      4.66           4.66Σg, lb.sub.m /ft.sup.3      0.075          0.075R.sub.F, in.      18             6ηoa    0.45           0.375______________________________________ 
    
     
         ______________________________________2. DETAIL GEOMETRY  Fan Designed  Using New Method                Conventional Fanr, in.   C, in.     γ°                        C, in.   γ°______________________________________14       13.11      15.06    5.5      2813.07    12.49      16.61    ↑  ↑12.13    11.87      18.17    ↑  ↑11.20    11.24      19.72    ↑  ↑9.86     10.33      21.82    ↑  ↑8.40     9.33       24.38    ↓ ↓7.46     8.69       25.93    ↓ ↓6.53     8.04       27.48    ↓ ↓5.59     7.40       29.03    ↓ ↓4.66     6.75       30.59    5.5      28______________________________________ PW = C sinγ= Projected Width 
    
     The results of test on a fan constructed as set forth in the example, as compared with a conventional sheet-metal blade as shown in FIGS. 4a and 4b, are illustrated in FIGS. 5 and 6.
A sheet metal fan blade of improved performance and efficiency has a varying camber angle and chord angle along radial positions of the blade, such that the angle of attack along at least 70% of the length of the blade is not less than 2deg or more than 10deg. The fan blade construction exhibits utility in an automotive radiator cooling system.