Galin Engine - Fan Laws - Google Sheets

	A	B	C	D	E	F	G	H	J	K	L	M	N
1
2				proportional to speed	2nd power of speed	3rd power of speed	55log10(n2/n1)		Summary
3	shaft 1 speed [RPM]	shaft 2 speed [RPM]	average speed [RPM]	volume flow	pressure	absorbed power	sound power level	linearising sound power level
4	2240	2240	2243	0.9988347989	0.9976709555	0.9965084682	-0.02784845004	0.9936081726	average speed	2243
5	2310	2170	2243	1.030048386	1.060999678	1.092881007	0.7071694357	1.176838705
6	2380	2110	2243	1.061261974	1.126276977	1.195274928	1.42024318	1.386833481	Volume flow:	qv2 = qv1 x (n2/n1)
7	2440	2040	2243	1.088016477	1.183779855	1.287971988	2.01495099	1.590358737	flow average	1	[]
8	2510	1980	2243	1.119230065	1.252675938	1.402032571	2.690565223	1.858046259	speed to get flow average	2243	RPM	no change
9	2570	1910	2243	1.145984568	1.313280631	1.504999337	3.254832325	2.115841994	conclusion:	there is no advantage to spinning at non-uniform speed on flow output of fan
10	2640	1850	2243	1.177198156	1.385795498	1.631355905	3.896726519	2.452859384
11	2700	1790	2243	1.203952659	1.449502006	1.745131795	4.43351757	2.775567267	Pressure:	p2 = p1 x (n2/n1)^2
12	2760	1730	2243	1.230707163	1.514640121	1.864078446	4.958510055	3.132210965	pressure average	1.23	[]
13	2810	1670	2243	1.253002583	1.570015472	1.967233441	5.387358136	3.457290029	speed to get pressure average	2762	RPM	higher
14	2870	1620	2243	1.279757086	1.637778199	2.095958256	5.892014862	3.883304859	conclusion:	the constant speed that a fan would need to develop to get the same pressure is higher, therefore there is advantage in running a fan at this non-uniform speed profile
15	2920	1560	2243	1.302052506	1.695340728	2.207422642	6.304567371	4.270283783
16	2970	1510	2243	1.324347925	1.753897427	2.322770419	6.710115254	4.688258238	Sound power level (CORRECTED):	PWL1 + 55log10(n2/n1)			Updated calculations for SPL
17	3020	1470	2243	1.346643345	1.813448298	2.442068083	7.108892404	5.1391257	Average (linear) sound power level:	4.5			- taking the average of the calculated dB values is a mistake.
18	3070	1420	2243	1.368938765	1.873993341	2.565382129	7.501121193	5.624865203	speed to get sound average	2953	RPM	31% higher.	The better way to do this is to calculate the linear value of the sound power level,
19	3110	1380	2243	1.3867751	1.923145179	2.666969848	7.810331938	6.039947919	SPL of GE fan:	6.6	dB		take the average, and then recalculate the SPL in dBs. Column H does this.
20	3150	1340	2243	1.404611436	1.972933286	2.771204656	8.115591	6.479762677	conclusion:	the perceived SPL of a fan running under the GE velocity profile will be 6.6dB higher.
21	3190	1300	2243	1.422447772	2.023357663	2.878120599	8.41699811	6.945440753
22	3230	1260	2243	1.440284107	2.07441831	2.987751724	8.71464927	7.43814991	Absorbed power:	pr1 x (n2/n1)^3
23	3260	1230	2243	1.453661359	2.113131347	3.071777386	8.935478545	7.826144359	power average	1.70	[]
24	3290	1190	2243	1.467038611	2.152202286	3.157363852	9.154284929	8.230543089	speed to get power average	3802	RPM	higher
25	3320	1160	2243	1.480415863	2.191631126	3.244525485	9.371105145	8.651880544	conclusion:	the constant speed that a fan would need to develop to get the same absorbed power is higher, hence it is not advantagous in terms of power use to run a fan at a non-constant speed
26	3350	1130	2243	1.493793114	2.231417869	3.333276648	9.585974929	9.090703494
27	3380	1110	2243	1.507170366	2.271562513	3.423631704	9.798929057	9.547571198	Fan Total Efficiency	(qv x ptF) / (10*Pr)
28	3400	1080	2243	1.516088534	2.298524443	3.484766553	9.939850979	9.862456436	GE fan	72.7%		lower
29	3430	1060	2243	1.529465786	2.33926559	3.577826684	10.14968714	10.350676	average fan	100.0%
30	3450	1030	2243	1.538383954	2.366625189	3.640778215	10.28856077	10.68700659	conclusion:	assuming a fan spinning at a uniform speed is 100% efficient, the relative efficiency of a fan driven by GE is 23% lower.
31	3470	1010	2243	1.547302122	2.394143855	3.704463866	10.42663166	11.03222639
32	3490	994	2243	1.556220289	2.421821589	3.768887894	10.56390902	11.38651709
33	3510	976	2243	1.565138457	2.44965839	3.834054554	10.70040195	11.75006299	Reference:	https://www.fantech.com.au/images/pdf/catalogue/fanlaws.pdf
34	3530	959	2243	1.574056625	2.477654259	3.899968101	10.83611934	12.12305104
35	3540	943	2243	1.578515709	2.491711844	3.933206287	10.90368995	12.31314504
36	3560	928	2243	1.587433877	2.519946313	4.000248146	11.03826043	12.70065278
37	3570	915	2243	1.591892961	2.534123198	4.034052881	11.10526243	12.89811494
38	3580	902	2243	1.596352045	2.548339851	4.068047531	11.17207701	13.09808187
39	3600	890	2243	1.605270213	2.576892455	4.136608699	11.30514808	13.50562878
40	3610	879	2243	1.609729296	2.591228408	4.171176282	11.37140665	13.71325856
41	3620	869	2243	1.61418838	2.605604127	4.205935906	11.43748192	13.92349272
42	3630	860	2243	1.618647464	2.620019614	4.240888104	11.50337492	14.13635659
43	3630	851	2243	1.618647464	2.620019614	4.240888104	11.50337492	14.13635659
44	3640	843	2243	1.623106548	2.634474867	4.276033408	11.56908664	14.3518757
45	3650	836	2243	1.627565632	2.648969887	4.311372349	11.63461809	14.57007572
46	3660	830	2243	1.632024716	2.663504674	4.346905459	11.69997024	14.79098252
47	3660	824	2243	1.632024716	2.663504674	4.346905459	11.69997024	14.79098252
48	3670	819	2243	1.6364838	2.678079228	4.382633271	11.76514408	15.01462215
49	3670	814	2243	1.6364838	2.678079228	4.382633271	11.76514408	15.01462215
50	3680	810	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
51	3680	806	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
52	3680	803	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
53	3680	801	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
54	3690	799	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498	Updated calculations for SPL
55	3690	797	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498	- taking the average of the calculated dB values is a mistake.
56	3690	796	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498	The better way to do this is to calculate the linear value of the sound power level,
57	3690	795	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498	take the average, and then recalculate the SPL in dBs. Column H does this.
58	3690	794	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
59	3690	794	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
60	3690	795	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
61	3690	795	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
62	3690	796	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
63	3690	798	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
64	3690	799	2243	1.645401968	2.707347636	4.454675127	11.89496068	15.47020498
65	3680	801	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
66	3680	803	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
67	3680	806	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
68	3680	809	2243	1.640942884	2.692693548	4.418556317	11.83014057	15.24102084
69	3670	812	2243	1.6364838	2.678079228	4.382633271	11.76514408	15.01462215
70	3670	815	2243	1.6364838	2.678079228	4.382633271	11.76514408	15.01462215
71	3670	819	2243	1.6364838	2.678079228	4.382633271	11.76514408	15.01462215
72	3660	822	2243	1.632024716	2.663504674	4.346905459	11.69997024	14.79098252
73	3660	826	2243	1.632024716	2.663504674	4.346905459	11.69997024	14.79098252
74	3650	831	2243	1.627565632	2.648969887	4.311372349	11.63461809	14.57007572
75	3650	835	2243	1.627565632	2.648969887	4.311372349	11.63461809	14.57007572
76	3650	840	2243	1.627565632	2.648969887	4.311372349	11.63461809	14.57007572
77	3640	845	2243	1.623106548	2.634474867	4.276033408	11.56908664	14.3518757
78	3640	850	2243	1.623106548	2.634474867	4.276033408	11.56908664	14.3518757
79	3630	856	2243	1.618647464	2.620019614	4.240888104	11.50337492	14.13635659
80	3620	861	2243	1.61418838	2.605604127	4.205935906	11.43748192	13.92349272
81	3620	867	2243	1.61418838	2.605604127	4.205935906	11.43748192	13.92349272
82	3610	873	2243	1.609729296	2.591228408	4.171176282	11.37140665	13.71325856
83	3610	879	2243	1.609729296	2.591228408	4.171176282	11.37140665	13.71325856
84	3600	885	2243	1.605270213	2.576892455	4.136608699	11.30514808	13.50562878
85	3590	892	2243	1.600811129	2.562596269	4.102232626	11.23870521	13.30057821
86	3590	899	2243	1.600811129	2.562596269	4.102232626	11.23870521	13.30057821
87	3580	906	2243	1.596352045	2.548339851	4.068047531	11.17207701	13.09808187
88	3570	913	2243	1.591892961	2.534123198	4.034052881	11.10526243	12.89811494
89	3570	920	2243	1.591892961	2.534123198	4.034052881	11.10526243	12.89811494
90	3560	927	2243	1.587433877	2.519946313	4.000248146	11.03826043	12.70065278
91	3550	935	2243	1.582974793	2.505809195	3.966632791	10.97106996	12.50567091
92	3540	943	2243	1.578515709	2.491711844	3.933206287	10.90368995	12.31314504
93	3530	951	2243	1.574056625	2.477654259	3.899968101	10.83611934	12.12305104
94	3530	959	2243	1.574056625	2.477654259	3.899968101	10.83611934	12.12305104
95	3520	967	2243	1.569597541	2.463636441	3.8669177	10.76835703	11.93536496
96	3510	975	2243	1.565138457	2.44965839	3.834054554	10.70040195	11.75006299
97	3500	984	2243	1.560679373	2.435720106	3.801378129	10.63225298	11.56712152
98	3490	993	2243	1.556220289	2.421821589	3.768887894	10.56390902	11.38651709
99	3480	1000	2243	1.551761205	2.407962839	3.736583317	10.49536896	11.20822643
100	3470	1010	2243	1.547302122	2.394143855	3.704463866	10.42663166	11.03222639