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Aerosol effects and climate, Part II: the role of nucleation and cosmic rays

Filed under: — group @ 15 April 2009 - (English)

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309 Responses to “Aerosol effects and climate, Part II: the role of nucleation and cosmic rays”

  1. 301
    Patrick 027 says:

    sample:

    r = interest rate on a lo-an: 7%
    f = inflation rate on all prices considered: 2%
    h = decay rate of solar panel performance (including loss of panel area): 1.5 %

    for a cost of $10/average W for a device at one time, paid with a lo-an:

    m0 (cents/kWh) (inflation adjusted constant price) required to pay off lo-an in time t (years):

    t(years), m0 (cents/kWh)

    15, 11.8
    20, 10
    25, 9.06
    30, 8.46
    40, 7.81
    50, 7.51
    60, 7.35
    70, 7.27
    80, 7.23
    100, 7.20
    infinite, 7.18

  2. 302
    Patrick 027 says:

    CORRECTION TO: comment 297 CORRECTION TO PART III:

    d/dt[exp(S*t)] = S*exp(S*t)

    d/dt[exp(H*t)] = H*exp(H*t)

    ——

    m*P*dt=L*N*dt

    m = L*(N/P)

    N in order to keep P increasing at rate S*P:

    N*dt = P*(S-H)*dt + N*dt*exp(-S*U)*exp(H*U)

    N*dt is necessary to increase P by P*S*dt while replacing the loss -P*H*dt and the retirement loss N*exp(-S*U)*dt * exp(H*U)

    N in order to keep P0 increasing at rate S*P0:

    N*dt = P0*(S-Hs)*dt + N*dt*exp(-S*U)*exp(Hs*U)

    ——

    N = P*(S-H) + N*exp[(H-S)*U]

    N * ( 1 – exp[(H-S)*U] ) = P*(S-H)

    —————

    m0/L0 = N/P = (S-H)/( 1 – exp[(H-S)*U] )

    P/N = ( 1 – exp[(H-S)*U] )/(S-H)

    P/P0
    =
    ( 1 – exp[(H-S)*U] )/(S-H)
    *
    (S-Hs)/( 1 – exp[(Hs-S)*U] )

    =
    (S-Hs)/(S-H) * ( 1 – exp[(H-S)*U] )/( 1 – exp[(Hs-S)*U] )

    ————–
    WHEN U GOES TO INFINITY:

    m0/L0 = N/P = (S-H)

    P/N = 1/(S-H)

    P/P0 = (S-Hs)/(S-H)

    ————–
    WHEN S GOES TO ZERO:

    m0/L0 = N/P = -H / ( 1 – exp[H*U] )

    P/N = – ( 1 – exp[H*U] ) / H

    P/P0
    =
    Hs/H * ( 1 – exp[H*U] )/( 1 – exp[Hs*U] )

  3. 303

    And from a different part of the sensitivity-to-nucleation spectrum: “Simulation of particle size distribution with a global aerosol model: contribution of nucleation to aerosol and CCN number concentrations” by F. Yu and G. Luo (http://www.atmos-chem-phys-discuss.net/9/10597/2009/acpd-9-10597-2009.html)

    Upon first glance, they find a much bigger contribution from nucleation to the CCN budget than others have reported. I haven’t read it in detail yet.

    Another interesting aerosol-climate paper is the following review about possible feedbacks of natural aerosol sources to a changing climate: Atmospheric aerosols in the earth system: a review of interactions and feedbacks (http://www.atmos-chem-phys-discuss.net/9/11087/2009/acpd-9-11087-2009.html)

    Both these papers are currently under (open) review.

  4. 304
    Hank Roberts says:

    Here, I think, is the abstract for the Pierce paper that was presented at the AGU (mentioned in the original post):

    Pierce, J. R.; Adams, P. J.
    Can cosmic rays affect cloud condensation nuclei by altering new particle formation rates?
    Geophys. Res. Lett., Vol. 36, No. 9, L09820
    http://dx.doi.org/10.1029/2009GL037946
    13 May 2009

  5. 305
    Patrick 027 says:

    CALCULATIONS FOR SOME SOLAR ELECTRICITY COSTS AND SOLAR COLLECTOR PERFORMANCE:

    EXPLANATIONS:

    ——————————————————–

    m0 is the price of electricity necessary to either:

    1.
    pay off debt by time t (with payments made over time as electricity sales revenue allows), where collectors are bought entirely with debt – with
    annual interest r = 7 %
    annual inflation f = 2 %
    and the same inflation rate applies to both electricity price m and collector price L

    2.
    pay for a rate of purchasing new collectors without any debt.

    ————-

    L0,the price per unit of collector, is $10 / average W

    Some combinations that result in $10 / average W

    (assuming high fill factors or concentration of sunlight into time intervals – more generally, that the average efficiency of conversion is not much lower than the rated efficiency of conversion ):

    $1.50 / peak W with average insolation of about 150 W/m2
    $1.70 / peak W with average insolation of about 170 W/m2
    $2.00 / peak W with average insolation of about 200 W/m2
    $2.50 / peak W with average insolation of about 250 W/m2
    $3.00 / peak W with average insolation of about 300 W/m2

    where the average insolation is the average solar power per unit area of collector; for geometric concentration, this only includes direct solar radiation (as opposed to diffuse radiation).

    ————-

    L0 and m0 are given in constant inflation-adjusted (real) values.

    m0 is linearly proportional to L0 – except in the case that L0 is changing while a debt is being paid for purchases based on previous L0 values. In the following, L0 is assumed constant.

    ——————————————————–

    P0 is a quantity of solar collectors measured by average power produced at installation (when new). When not otherwise specified, P0 refers to the quantity of collectors currently in operation at a time t, and can be used as a relative measure of the area of collectors and (with adjustment for collector orientations and spacing) a relative measure of the area occupied by collectors.

    P is the average power produced by collectors in operation at a time t.

    Thus,

    P/P0 is the average efficiency of operational collectors relative to efficiency of new collectors,

    and

    P0/P is the area required per unit average power supply relative to the area per unit average power supply for new collectors.

    Some maintenance and other costs could be proportional to the area of the collectors and the area they occupy, so it is of interest to know P0/P and P/P0.

    —————-

    -h, -he, and -hs are annual fractional losses.

    (h, he, and hs are defined as gains, they have negative values.)

    -h is the annual fractional loss in average power P produced by a set of collectors since and includes the effects of decreases in performance of collectors in operation and the loss of collectors from operation (such as from severe storm damage or fire), but not including retirement of collectors at a set age.

    -hs is the annual fractional loss in operational P0 (the loss of operational collectors from collectors in operation) that is not due to retirement at a set age.

    -he is the annual fractional loss in P from operational P0 that remains operational.

    For small h, he, and hs values, h is approximately equal to the sum of he and hs.

    The same set of h, he, and hs values are used for each table where applicable; those used in the calculations for a table are restated for that table for convenience.

    —————

    Where applicable, the retirement age U of operational collectors was chosen as the time when performance (P per unit operational P0) will have dropped by a factor of e from the initial value (P/P0 = 1 for newly installed collectors).
    ——————————————————–

    CASES CONSIDERED:

    I. ONE TIME INSTALLMENT at time t = 0

    A set of collectors (of quantity “installed P0”) is bought and installed at time t = 0.

    Cummulative Energy since installation / installed P0, [(W*yr) / W] = years
    – this is the time in years it would take for a set of collectors with constant P (h = 0) to produce the same energy that a set of actual collectors (with nonzero h) would produce from installation at time 0 to time t.

    Average ( P/ installed P0 ) from installation to time t since installation
    – this is the Cummulative Energy at time t per unit P0 divided by the time t.

    —————————

    II. Continual purchasing and installation of new collectors at a rate N = new P0 per unit time, measured in (W/year).

    A. CONSTANT N

    N = 1 installed W per year.

    Starting at time t = 0, where P and P0 at time t=0 are both 0.

    Operational collectors installed at time t = ti are retired at time ti + U, where U is the retirement age.

    ————-

    B. EXPONENTIAL GROWTH with Retirement at U

    P, operational P0, and N all increase exponentially,

    where s is the annual fractional increase.

    There is a retirement age of U as in the case “CONSTANT N”.

    It is assumed that exponential growth has been ongoing for some time so that retirements are already occuring at time t = 0.

    ————-

    C. EXPONENTIAL GROWTH, no retirement at a set age

    As above, but without a retirement age – the only loss of operational P0 is from nonzero hs.

    ————-

    For both EXPONENTIAL cases:

    For any starting situation, the ratio of P to N and P0 to N will tend to approach constant values over time if N is increasing exponentially, so that P and P0 will eventually increase at the same rate s.

    IF P and P0 = 0 at time t and N starts at some nonzero number and increases exponentially, P/N and P0/N will start at 0 and increase over time.

    To create a situation where the calcuations for the cases above would apply immediately, one could initially buy and install some P0 at time t = 0, and then increase P and N exponentially from then on; in that case, the calculation of m0 would not include the initial purchase, and there would be a discontinuity at time t = U if there are retirements.

    ——————————————————–
    Formulas used are found at:

    295
    http://www.realclimate.org/index.php/archives/2009/04/aerosol-effects-and-climate-part-ii-the-role-of-nucleation-and-cosmic-rays/langswitch_lang/it#comment-123843

    Note corrections to PART III in:

    302
    http://www.realclimate.org/index.php/archives/2009/04/aerosol-effects-and-climate-part-ii-the-role-of-nucleation-and-cosmic-rays/langswitch_lang/it#comment-125193

    ________________________________________________________________________________________

    PRICE OF ELECTRICITY FOR PAYING OFF DEBT BY TIME t, WHERE COLLECTORS ARE BOUGHT or FIRST BOUGHT AT t = 0:

    ___________________________________________

    ONE TIME INSTALLMENT

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ m0 , (cents/kWh)
    _ _ _ _ _|___ to pay off debt at time t
    _____ 15 |_ 11.02 ,_ 11.16 ,_ 11.38 ,_ 11.53 ,_ 11.75 ,_ 12.14
    _____ 20 |__ 9.24 ,__ 9.40 ,__ 9.63 ,__ 9.79 ,_ 10.03 ,_ 10.44
    _____ 25 |__ 8.22 ,__ 8.39 ,__ 8.64 ,__ 8.80 ,__ 9.06 ,__ 9.50
    _____ 30 |__ 7.58 ,__ 7.76 ,__ 8.02 ,__ 8.19 ,__ 8.46 ,__ 8.92
    _____ 40 |__ 6.86 ,__ 7.04 ,__ 7.33 ,__ 7.52 ,__ 7.81 ,__ 8.31
    _____ 50 |__ 6.49 ,__ 6.69 ,__ 6.99 ,__ 7.20 ,__ 7.51 ,__ 8.03
    _____ 60 |__ 6.29 ,__ 6.50 ,__ 6.82 ,__ 7.03 ,__ 7.35 ,__ 7.90
    _____ 70 |__ 6.18 ,__ 6.40 ,__ 6.72 ,__ 6.94 ,__ 7.27 ,__ 7.83
    _____ 80 |__ 6.12 ,__ 6.34 ,__ 6.67 ,__ 6.89 ,__ 7.23 ,__ 7.80
    _____ 90 |__ 6.08 ,__ 6.31 ,__ 6.64 ,__ 6.87 ,__ 7.21 ,__ 7.78
    ____ 100 |__ 6.06 ,__ 6.29 ,__ 6.63 ,__ 6.85 ,__ 7.20 ,__ 7.77
    ____ 120 |__ 6.04 ,__ 6.27 ,__ 6.61 ,__ 6.84 ,__ 7.19 ,__ 7.77
    ____ 150 |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.18 ,__ 7.76
    ____ 200 |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.18 ,__ 7.76
    ____ 250 |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.18 ,__ 7.76
    ____ INF |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.18 ,__ 7.76

    ___________________________________________

    CONSTANT N

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ m0 , (cents/kWh)
    _ _ _ _ _|___ to pay off debt at time t
    _____ 15 |_ 17.67 ,_ 17.83 ,_ 18.08 ,_ 18.25 ,_ 18.50 ,_ 18.93
    _____ 20 |_ 13.95 ,_ 14.12 ,_ 14.38 ,_ 14.55 ,_ 14.81 ,_ 15.25
    _____ 25 |_ 11.76 ,_ 11.93 ,_ 12.20 ,_ 12.37 ,_ 12.64 ,_ 13.09
    _____ 30 |_ 10.33 ,_ 10.51 ,_ 10.78 ,_ 10.96 ,_ 11.23 ,_ 11.70
    _____ 40 |__ 8.62 ,__ 8.80 ,__ 9.08 ,__ 9.27 ,__ 9.56 ,_ 10.05
    _____ 50 |__ 7.66 ,__ 7.85 ,__ 8.15 ,__ 8.34 ,__ 8.64 ,__ 9.15
    _____ 60 |__ 7.09 ,__ 7.29 ,__ 7.59 ,__ 7.79 ,__ 8.10 ,__ 8.63
    _____ 70 |__ 6.72 ,__ 6.93 ,__ 7.24 ,__ 7.45 ,__ 7.77 ,__ 8.31
    _____ 80 |__ 6.49 ,__ 6.70 ,__ 7.02 ,__ 7.23 ,__ 7.56 ,__ 8.11
    _____ 90 |__ 6.33 ,__ 6.55 ,__ 6.87 ,__ 7.09 ,__ 7.42 ,__ 7.98
    ____ 100 |__ 6.23 ,__ 6.45 ,__ 6.78 ,__ 7.00 ,__ 7.34 ,__ 7.90
    ____ 120 |__ 6.12 ,__ 6.34 ,__ 6.68 ,__ 6.90 ,__ 7.25 ,__ 7.82
    ____ 150 |__ 6.05 ,__ 6.28 ,__ 6.62 ,__ 6.85 ,__ 7.20 ,__ 7.78
    ____ 200 |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.19 ,__ 7.77
    ____ 250 |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.19 ,__ 7.77
    ____ INF |__ 6.03 ,__ 6.26 ,__ 6.61 ,__ 6.84 ,__ 7.18 ,__ 7.76

    ________________________________________________________________________________________

    PRICE OF ELECTRICITY FOR PAYING FOR NEW COLLECTORS, NO DEBT:

    ___________________________________________

    CONSTANT N

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ m0 , (cents/kWh)
    _ _ _ _ _|___ to pay for new collectors, no debt
    _____ 15 |__ 7.89 ,__ 8.01 ,__ 8.19 ,__ 8.31 ,__ 8.50 ,__ 8.82
    _____ 20 |__ 5.99 ,__ 6.11 ,__ 6.30 ,__ 6.42 ,__ 6.61 ,__ 6.93
    _____ 25 |__ 4.85 ,__ 4.98 ,__ 5.16 ,__ 5.29 ,__ 5.48 ,__ 5.81
    _____ 30 |__ 4.10 ,__ 4.22 ,__ 4.40 ,__ 4.53 ,__ 4.73 ,__ 5.07
    _____ 40 |__ 3.15 ,__ 3.27 ,__ 3.46 ,__ 3.60 ,__ 3.80 ,__ 4.16
    _____ 50 |__ 2.58 ,__ 2.71 ,__ 2.90 ,__ 3.04 ,__ 3.25 ,__ 3.62
    _____ 60 |__ 2.20 ,__ 2.33 ,__ 2.53 ,__ 2.67 ,__ 2.89 ,__ 3.28
    _____ 70 |__ 1.93 ,__ 2.06 ,__ 2.27 ,__ 2.41 ,__ 2.64 ,__ 3.04
    _____ 80 |__ 1.73 ,__ 1.86 ,__ 2.08 ,__ 2.22 ,__ 2.46 ,__ 2.88
    _____ 90 |__ 1.57 ,__ 1.71 ,__ 1.93 ,__ 2.08 ,__ 2.32 ,__ 2.75
    ____ 100 |__ 1.45 ,__ 1.59 ,__ 1.81 ,__ 1.96 ,__ 2.21 ,__ 2.67
    ____ 120 |__ 1.27 ,__ 1.41 ,__ 1.64 ,__ 1.80 ,__ 2.06 ,__ 2.67
    ____ 150 |__ 1.08 ,__ 1.23 ,__ 1.47 ,__ 1.65 ,__ 2.00 ,__ 2.67
    ____ 200 |__ 0.90 ,__ 1.06 ,__ 1.33 ,__ 1.59 ,__ 2.00 ,__ 2.67
    ____ 250 |__ 0.85 ,__ 1.06 ,__ 1.33 ,__ 1.59 ,__ 2.00 ,__ 2.67
    ____ INF |__ 0.85 ,__ 1.06 ,__ 1.33 ,__ 1.59 ,__ 2.00 ,__ 2.67

    ___________________________________________

    EXPONENTIAL GROWTH with Retirement at U

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | m0 , (cents/kWh) _____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ to pay for new collectors, no debt______ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 |__ 0.85 ,__ 1.06 ,__ 1.33 ,__ 1.59 ,__ 2.00 ,__ 2.67 |_ 0.0 |
    ____ 0.1 |__ 0.93 ,__ 1.15 ,__ 1.42 ,__ 1.69 ,__ 2.09 ,__ 2.76 |_ 0.1 | 2303.7
    ____ 0.2 |__ 1.01 ,__ 1.23 ,__ 1.51 ,__ 1.78 ,__ 2.18 ,__ 2.85 |_ 0.2 | 1152.4
    ____ 0.5 |__ 1.28 ,__ 1.51 ,__ 1.81 ,__ 2.07 ,__ 2.47 ,__ 3.14 |_ 0.5 |_ 461.7
    ____ 1.0 |__ 1.77 ,__ 2.00 ,__ 2.33 ,__ 2.58 ,__ 2.97 ,__ 3.63 |_ 1.0 |_ 231.4
    ____ 1.5 |__ 2.30 ,__ 2.53 ,__ 2.87 ,__ 3.11 ,__ 3.49 ,__ 4.13 |_ 1.5 |_ 154.7
    ____ 2.0 |__ 2.84 ,__ 3.08 ,__ 3.41 ,__ 3.66 ,__ 4.02 ,__ 4.65 |_ 2.0 |_ 116.3
    ____ 3.0 |__ 3.95 ,__ 4.18 ,__ 4.52 ,__ 4.75 ,__ 5.11 ,__ 5.72 |_ 3.0 |__ 77.9
    ____ 4.0 |__ 5.05 ,__ 5.28 ,__ 5.62 ,__ 5.85 ,__ 6.20 ,__ 6.80 |_ 4.0 |__ 58.7
    ____ 5.0 |__ 6.14 ,__ 6.37 ,__ 6.71 ,__ 6.94 ,__ 7.29 ,__ 7.88 |_ 5.0 |__ 47.2
    ____ 6.0 |__ 7.22 ,__ 7.45 ,__ 7.79 ,__ 8.02 ,__ 8.37 ,__ 8.96 |_ 6.0 |__ 39.5
    ____ 7.0 |__ 8.29 ,__ 8.52 ,__ 8.86 ,__ 9.10 ,__ 9.44 ,_ 10.02 |_ 7.0 |__ 34.0
    ____ 8.0 |__ 9.35 ,__ 9.58 ,__ 9.93 ,_ 10.16 ,_ 10.50 ,_ 11.08 |_ 8.0 |__ 29.9
    ____ 9.0 |_ 10.40 ,_ 10.63 ,_ 10.98 ,_ 11.21 ,_ 11.56 ,_ 12.14 |_ 9.0 |__ 26.7
    ___ 10.0 |_ 11.44 ,_ 11.67 ,_ 12.02 ,_ 12.25 ,_ 12.60 ,_ 13.18 | 10.0 |__ 24.2
    ___ 15.0 |_ 16.52 ,_ 16.74 ,_ 17.09 ,_ 17.32 ,_ 17.67 ,_ 18.25 | 15.0 |__ 16.5
    ___ 20.0 |_ 21.37 ,_ 21.60 ,_ 21.95 ,_ 22.18 ,_ 22.52 ,_ 23.10 | 20.0 |__ 12.6
    ___ 30.0 |_ 30.50 ,_ 30.73 ,_ 31.08 ,_ 31.31 ,_ 31.65 ,_ 32.23 | 30.0 |___ 8.8

    ___________________________________________

    EXPONENTIAL GROWTH, no retirement at a set age

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | m0 , (cents/kWh) _____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ to pay for new collectors, no debt______ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 |__ 0.57 ,__ 0.80 ,__ 1.15 ,__ 1.38 ,__ 1.72 ,__ 2.30 |_ 0.0 |
    ____ 0.1 |__ 0.69 ,__ 0.92 ,__ 1.26 ,__ 1.49 ,__ 1.84 ,__ 2.42 |_ 0.1 | 2303.7
    ____ 0.2 |__ 0.80 ,__ 1.03 ,__ 1.37 ,__ 1.61 ,__ 1.95 ,__ 2.53 |_ 0.2 | 1152.4
    ____ 0.5 |__ 1.14 ,__ 1.37 ,__ 1.72 ,__ 1.95 ,__ 2.29 ,__ 2.87 |_ 0.5 |_ 461.7
    ____ 1.0 |__ 1.71 ,__ 1.94 ,__ 2.28 ,__ 2.51 ,__ 2.86 ,__ 3.44 |_ 1.0 |_ 231.4
    ____ 1.5 |__ 2.27 ,__ 2.50 ,__ 2.84 ,__ 3.08 ,__ 3.42 ,__ 4.00 |_ 1.5 |_ 154.7
    ____ 2.0 |__ 2.83 ,__ 3.06 ,__ 3.41 ,__ 3.64 ,__ 3.98 ,__ 4.56 |_ 2.0 |_ 116.3
    ____ 3.0 |__ 3.94 ,__ 4.17 ,__ 4.52 ,__ 4.75 ,__ 5.10 ,__ 5.68 |_ 3.0 |__ 77.9
    ____ 4.0 |__ 5.05 ,__ 5.28 ,__ 5.62 ,__ 5.85 ,__ 6.20 ,__ 6.78 |_ 4.0 |__ 58.7
    ____ 5.0 |__ 6.14 ,__ 6.37 ,__ 6.71 ,__ 6.94 ,__ 7.29 ,__ 7.87 |_ 5.0 |__ 47.2
    ____ 6.0 |__ 7.22 ,__ 7.45 ,__ 7.79 ,__ 8.02 ,__ 8.37 ,__ 8.95 |_ 6.0 |__ 39.5
    ____ 7.0 |__ 8.29 ,__ 8.52 ,__ 8.86 ,__ 9.10 ,__ 9.44 ,_ 10.02 |_ 7.0 |__ 34.0
    ____ 8.0 |__ 9.35 ,__ 9.58 ,__ 9.93 ,_ 10.16 ,_ 10.50 ,_ 11.08 |_ 8.0 |__ 29.9
    ____ 9.0 |_ 10.40 ,_ 10.63 ,_ 10.98 ,_ 11.21 ,_ 11.56 ,_ 12.14 |_ 9.0 |__ 26.7
    ___ 10.0 |_ 11.44 ,_ 11.67 ,_ 12.02 ,_ 12.25 ,_ 12.60 ,_ 13.18 | 10.0 |__ 24.2
    ___ 15.0 |_ 16.52 ,_ 16.74 ,_ 17.09 ,_ 17.32 ,_ 17.67 ,_ 18.25 | 15.0 |__ 16.5
    ___ 20.0 |_ 21.37 ,_ 21.60 ,_ 21.95 ,_ 22.18 ,_ 22.52 ,_ 23.10 | 20.0 |__ 12.6
    ___ 30.0 |_ 30.50 ,_ 30.73 ,_ 31.08 ,_ 31.31 ,_ 31.65 ,_ 32.23 | 30.0 |___ 8.8

    _________________________________________________________________________________________

    OTHER CALCULATIONS:

    ___________________________________________

    ONE TIME INSTALLMENT

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ P / installed P0
    _ _ _ _ _|___
    _____ 15 |__ 0.93 ,__ 0.90 ,__ 0.86 ,__ 0.83 ,__ 0.80 ,__ 0.74
    _____ 20 |__ 0.90 ,__ 0.87 ,__ 0.82 ,__ 0.79 ,__ 0.74 ,__ 0.67
    _____ 25 |__ 0.88 ,__ 0.84 ,__ 0.78 ,__ 0.74 ,__ 0.69 ,__ 0.60
    _____ 30 |__ 0.86 ,__ 0.81 ,__ 0.74 ,__ 0.70 ,__ 0.64 ,__ 0.55
    _____ 40 |__ 0.82 ,__ 0.76 ,__ 0.67 ,__ 0.62 ,__ 0.55 ,__ 0.45
    _____ 50 |__ 0.78 ,__ 0.70 ,__ 0.61 ,__ 0.55 ,__ 0.47 ,__ 0.36
    _____ 60 |__ 0.74 ,__ 0.66 ,__ 0.55 ,__ 0.48 ,__ 0.40 ,__ 0.30
    _____ 70 |__ 0.70 ,__ 0.61 ,__ 0.49 ,__ 0.43 ,__ 0.35 ,__ 0.24
    _____ 80 |__ 0.67 ,__ 0.57 ,__ 0.45 ,__ 0.38 ,__ 0.30 ,__ 0.20
    _____ 90 |__ 0.64 ,__ 0.53 ,__ 0.40 ,__ 0.34 ,__ 0.26 ,__ 0.16
    ____ 100 |__ 0.61 ,__ 0.50 ,__ 0.37 ,__ 0.30 ,__ 0.22 ,__ 0.13
    ____ 120 |__ 0.55 ,__ 0.43 ,__ 0.30 ,__ 0.23 ,__ 0.16 ,__ 0.09
    ____ 150 |__ 0.47 ,__ 0.35 ,__ 0.22 ,__ 0.16 ,__ 0.10 ,__ 0.05
    ____ 200 |__ 0.37 ,__ 0.25 ,__ 0.13 ,__ 0.09 ,__ 0.05 ,__ 0.02
    ____ 250 |__ 0.29 ,__ 0.17 ,__ 0.08 ,__ 0.05 ,__ 0.02 ,__ 0.01
    ___ 1000 |__ 0.01 ,__ 0.00 ,__ 0.00 ,__ 0.00 ,__ 0.00 ,__ 0.00

    _ -he (%):__ 0.45 ,__ 0.50 ,__ 0.50 ,__ 0.60 ,__ 0.76 ,__ 1.01
    _ _ _ _ _|____________________________________________________
    t, years |_ P / operational P0
    _ _ _ _ _|___
    _____ 15 |__ 0.93 ,__ 0.93 ,__ 0.93 ,__ 0.91 ,__ 0.89 ,__ 0.86
    _____ 20 |__ 0.91 ,__ 0.90 ,__ 0.90 ,__ 0.89 ,__ 0.86 ,__ 0.82
    _____ 25 |__ 0.89 ,__ 0.88 ,__ 0.88 ,__ 0.86 ,__ 0.83 ,__ 0.78
    _____ 30 |__ 0.87 ,__ 0.86 ,__ 0.86 ,__ 0.83 ,__ 0.80 ,__ 0.74
    _____ 40 |__ 0.83 ,__ 0.82 ,__ 0.82 ,__ 0.78 ,__ 0.74 ,__ 0.67
    _____ 50 |__ 0.80 ,__ 0.78 ,__ 0.78 ,__ 0.74 ,__ 0.68 ,__ 0.60
    _____ 60 |__ 0.76 ,__ 0.74 ,__ 0.74 ,__ 0.70 ,__ 0.63 ,__ 0.54
    _____ 70 |__ 0.73 ,__ 0.70 ,__ 0.70 ,__ 0.65 ,__ 0.59 ,__ 0.49
    _____ 80 |__ 0.70 ,__ 0.67 ,__ 0.67 ,__ 0.62 ,__ 0.55 ,__ 0.44
    _____ 90 |__ 0.67 ,__ 0.64 ,__ 0.64 ,__ 0.58 ,__ 0.51 ,__ 0.40
    ____ 100 |__ 0.64 ,__ 0.61 ,__ 0.60 ,__ 0.55 ,__ 0.47 ,__ 0.36
    ____ 120 |__ 0.58 ,__ 0.55 ,__ 0.55 ,__ 0.48 ,__ 0.40 ,__ 0.30
    ____ 150 |__ 0.51 ,__ 0.47 ,__ 0.47 ,__ 0.40 ,__ 0.32 ,__ 0.22
    ____ 200 |__ 0.41 ,__ 0.37 ,__ 0.37 ,__ 0.30 ,__ 0.22 ,__ 0.13
    ____ 250 |__ 0.32 ,__ 0.28 ,__ 0.28 ,__ 0.22 ,__ 0.15 ,__ 0.08
    ___ 1000 |__ 0.01 ,__ 0.01 ,__ 0.01 ,__ 0.00 ,__ 0.00 ,__ 0.00

    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    _ _ _ _ _|____________________________________________________
    t, years |_ operational P0 / installed P0
    _ _ _ _ _|___
    _____ 15 |__ 0.99 ,__ 0.97 ,__ 0.93 ,__ 0.91 ,__ 0.89 ,__ 0.86
    _____ 20 |__ 0.99 ,__ 0.96 ,__ 0.90 ,__ 0.89 ,__ 0.86 ,__ 0.82
    _____ 25 |__ 0.99 ,__ 0.95 ,__ 0.88 ,__ 0.86 ,__ 0.83 ,__ 0.78
    _____ 30 |__ 0.99 ,__ 0.94 ,__ 0.86 ,__ 0.83 ,__ 0.80 ,__ 0.74
    _____ 40 |__ 0.98 ,__ 0.92 ,__ 0.82 ,__ 0.79 ,__ 0.74 ,__ 0.67
    _____ 50 |__ 0.98 ,__ 0.90 ,__ 0.78 ,__ 0.74 ,__ 0.69 ,__ 0.61
    _____ 60 |__ 0.97 ,__ 0.89 ,__ 0.74 ,__ 0.70 ,__ 0.64 ,__ 0.55
    _____ 70 |__ 0.97 ,__ 0.87 ,__ 0.70 ,__ 0.66 ,__ 0.59 ,__ 0.49
    _____ 80 |__ 0.96 ,__ 0.85 ,__ 0.67 ,__ 0.62 ,__ 0.55 ,__ 0.45
    _____ 90 |__ 0.96 ,__ 0.84 ,__ 0.64 ,__ 0.58 ,__ 0.51 ,__ 0.40
    ____ 100 |__ 0.95 ,__ 0.82 ,__ 0.61 ,__ 0.55 ,__ 0.47 ,__ 0.37
    ____ 120 |__ 0.94 ,__ 0.79 ,__ 0.55 ,__ 0.49 ,__ 0.41 ,__ 0.30
    ____ 150 |__ 0.93 ,__ 0.74 ,__ 0.47 ,__ 0.41 ,__ 0.32 ,__ 0.22
    ____ 200 |__ 0.90 ,__ 0.67 ,__ 0.37 ,__ 0.30 ,__ 0.22 ,__ 0.13
    ____ 250 |__ 0.88 ,__ 0.61 ,__ 0.29 ,__ 0.22 ,__ 0.15 ,__ 0.08
    ___ 1000 |__ 0.61 ,__ 0.14 ,__ 0.01 ,__ 0.00 ,__ 0.00 ,__ 0.00

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ Cummulative Energy since installation / installed P0, [(W*yr) / W] = years
    _ _ _ _ _|___
    _____ 15 |_ 14.45 ,_ 14.24 ,_ 13.92 ,_ 13.72 ,_ 13.42 ,_ 12.94
    _____ 20 |_ 19.03 ,_ 18.66 ,_ 18.12 ,_ 17.77 ,_ 17.26 ,_ 16.45
    _____ 25 |_ 23.50 ,_ 22.93 ,_ 22.11 ,_ 21.58 ,_ 20.82 ,_ 19.63
    _____ 30 |_ 27.85 ,_ 27.05 ,_ 25.90 ,_ 25.17 ,_ 24.12 ,_ 22.50
    _____ 40 |_ 36.25 ,_ 34.87 ,_ 32.94 ,_ 31.73 ,_ 30.02 ,_ 27.44
    _____ 50 |_ 44.23 ,_ 42.16 ,_ 39.30 ,_ 37.54 ,_ 35.09 ,_ 31.47
    _____ 60 |_ 51.82 ,_ 48.96 ,_ 45.06 ,_ 42.69 ,_ 39.45 ,_ 34.77
    _____ 70 |_ 59.04 ,_ 55.30 ,_ 50.26 ,_ 47.25 ,_ 43.20 ,_ 37.46
    _____ 80 |_ 65.91 ,_ 61.20 ,_ 54.97 ,_ 51.30 ,_ 46.42 ,_ 39.67
    _____ 90 |_ 72.44 ,_ 66.71 ,_ 59.23 ,_ 54.89 ,_ 49.19 ,_ 41.46
    ____ 100 |_ 78.65 ,_ 71.84 ,_ 63.08 ,_ 58.06 ,_ 51.57 ,_ 42.93
    ____ 120 |_ 90.18 ,_ 81.08 ,_ 69.71 ,_ 63.38 ,_ 55.38 ,_ 45.12
    ____ 150 | 105.44 ,_ 92.72 ,_ 77.46 ,_ 69.29 ,_ 59.31 ,_ 47.11
    ____ 200 | 126.29 , 107.42 ,_ 86.17 ,_ 75.43 ,_ 62.95 ,_ 48.63
    ____ 250 | 142.52 , 117.77 ,_ 91.43 ,_ 78.78 ,_ 64.65 ,_ 49.18
    ____ INF | 199.50 , 142.36 ,_ 99.50 ,_ 82.83 ,_ 66.17 ,_ 49.50

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ Average ( P/ installed P0 ) from installation to time t since installation
    _ _ _ _ _|___
    _____ 15 |__ 0.96 ,__ 0.95 ,__ 0.93 ,__ 0.91 ,__ 0.89 ,__ 0.86
    _____ 20 |__ 0.95 ,__ 0.93 ,__ 0.91 ,__ 0.89 ,__ 0.86 ,__ 0.82
    _____ 25 |__ 0.94 ,__ 0.92 ,__ 0.88 ,__ 0.86 ,__ 0.83 ,__ 0.79
    _____ 30 |__ 0.93 ,__ 0.90 ,__ 0.86 ,__ 0.84 ,__ 0.80 ,__ 0.75
    _____ 40 |__ 0.91 ,__ 0.87 ,__ 0.82 ,__ 0.79 ,__ 0.75 ,__ 0.69
    _____ 50 |__ 0.88 ,__ 0.84 ,__ 0.79 ,__ 0.75 ,__ 0.70 ,__ 0.63
    _____ 60 |__ 0.86 ,__ 0.82 ,__ 0.75 ,__ 0.71 ,__ 0.66 ,__ 0.58
    _____ 70 |__ 0.84 ,__ 0.79 ,__ 0.72 ,__ 0.68 ,__ 0.62 ,__ 0.54
    _____ 80 |__ 0.82 ,__ 0.77 ,__ 0.69 ,__ 0.64 ,__ 0.58 ,__ 0.50
    _____ 90 |__ 0.80 ,__ 0.74 ,__ 0.66 ,__ 0.61 ,__ 0.55 ,__ 0.46
    ____ 100 |__ 0.79 ,__ 0.72 ,__ 0.63 ,__ 0.58 ,__ 0.52 ,__ 0.43
    ____ 120 |__ 0.75 ,__ 0.68 ,__ 0.58 ,__ 0.53 ,__ 0.46 ,__ 0.38
    ____ 150 |__ 0.70 ,__ 0.62 ,__ 0.52 ,__ 0.46 ,__ 0.40 ,__ 0.31
    ____ 200 |__ 0.63 ,__ 0.54 ,__ 0.43 ,__ 0.38 ,__ 0.31 ,__ 0.24
    ____ 250 |__ 0.57 ,__ 0.47 ,__ 0.37 ,__ 0.32 ,__ 0.26 ,__ 0.20
    ___ 1000 |__ 0.00 ,__ 0.00 ,__ 0.00 ,__ 0.00 ,__ 0.00 ,__ 0.00

    ___________________________________________

    CONSTANT N

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ P/N , [W / (W/yr)] = years
    _ _ _ _ _|___
    _____ 15 |_ 14.45 ,_ 14.24 ,_ 13.92 ,_ 13.72 ,_ 13.42 ,_ 12.94
    _____ 20 |_ 19.03 ,_ 18.66 ,_ 18.12 ,_ 17.77 ,_ 17.26 ,_ 16.45
    _____ 25 |_ 23.50 ,_ 22.93 ,_ 22.11 ,_ 21.58 ,_ 20.82 ,_ 19.63
    _____ 30 |_ 27.85 ,_ 27.05 ,_ 25.90 ,_ 25.17 ,_ 24.12 ,_ 22.50
    _____ 40 |_ 36.25 ,_ 34.87 ,_ 32.94 ,_ 31.73 ,_ 30.02 ,_ 27.44
    _____ 50 |_ 44.23 ,_ 42.16 ,_ 39.30 ,_ 37.54 ,_ 35.09 ,_ 31.47
    _____ 60 |_ 51.82 ,_ 48.96 ,_ 45.06 ,_ 42.69 ,_ 39.45 ,_ 34.77
    _____ 70 |_ 59.04 ,_ 55.30 ,_ 50.26 ,_ 47.25 ,_ 43.20 ,_ 37.46
    _____ 80 |_ 65.91 ,_ 61.20 ,_ 54.97 ,_ 51.30 ,_ 46.42 ,_ 39.67
    _____ 90 |_ 72.44 ,_ 66.71 ,_ 59.23 ,_ 54.89 ,_ 49.19 ,_ 41.46
    ____ 100 |_ 78.65 ,_ 71.84 ,_ 63.08 ,_ 58.06 ,_ 51.57 ,_ 42.73
    ____ 120 |_ 90.18 ,_ 81.08 ,_ 69.71 ,_ 63.38 ,_ 55.38 ,_ 42.73
    ____ 150 | 105.44 ,_ 92.72 ,_ 77.46 ,_ 69.29 ,_ 57.14 ,_ 42.73
    ____ 200 | 126.29 , 107.20 ,_ 85.97 ,_ 71.55 ,_ 57.14 ,_ 42.73
    ____ 250 | 133.81 , 107.20 ,_ 85.97 ,_ 71.55 ,_ 57.14 ,_ 42.73
    ___ 1000 | 133.81 , 107.20 ,_ 85.97 ,_ 71.55 ,_ 57.14 ,_ 42.73

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    _ _ _ _ _|____________________________________________________
    t, years |_ operational P0 / N , [W / (W/yr)] = years
    _ _ _ _ _|___
    _____ 15 |_ 14.94 ,_ 14.78 ,_ 14.45 ,_ 14.34 ,_ 14.18 ,_ 13.92
    _____ 20 |_ 19.90 ,_ 19.60 ,_ 19.03 ,_ 18.84 ,_ 18.57 ,_ 18.12
    _____ 25 |_ 24.84 ,_ 24.38 ,_ 23.50 ,_ 23.21 ,_ 22.79 ,_ 22.11
    _____ 30 |_ 29.78 ,_ 29.12 ,_ 27.85 ,_ 27.45 ,_ 26.85 ,_ 25.90
    _____ 40 |_ 39.60 ,_ 38.44 ,_ 36.25 ,_ 35.55 ,_ 34.54 ,_ 32.94
    _____ 50 |_ 49.38 ,_ 47.58 ,_ 44.23 ,_ 43.18 ,_ 41.67 ,_ 39.30
    _____ 60 |_ 59.11 ,_ 56.54 ,_ 51.82 ,_ 50.36 ,_ 48.28 ,_ 45.06
    _____ 70 |_ 68.79 ,_ 65.32 ,_ 59.04 ,_ 57.13 ,_ 54.41 ,_ 50.26
    _____ 80 |_ 78.42 ,_ 73.92 ,_ 65.91 ,_ 63.49 ,_ 60.10 ,_ 54.97
    _____ 90 |_ 88.00 ,_ 82.36 ,_ 72.44 ,_ 69.49 ,_ 65.37 ,_ 59.23
    ____ 100 |_ 97.54 ,_ 90.63 ,_ 78.65 ,_ 75.14 ,_ 70.26 ,_ 62.53
    ____ 120 | 116.47 , 106.67 ,_ 90.18 ,_ 85.46 ,_ 79.01 ,_ 62.53
    ____ 150 | 144.51 , 129.57 , 105.44 ,_ 98.79 ,_ 83.60 ,_ 62.53
    ____ 200 | 190.32 , 164.21 , 125.74 , 104.67 ,_ 83.60 ,_ 62.53
    ____ 250 | 209.77 , 164.21 , 125.74 , 104.67 ,_ 83.60 ,_ 62.53
    ___ 1000 | 209.77 , 164.21 , 125.74 , 104.67 ,_ 83.60 ,_ 62.53

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ P / operational P0
    _ _ _ _ _|___
    _____ 15 |__ 0.97 ,__ 0.96 ,__ 0.96 ,__ 0.96 ,__ 0.95 ,__ 0.93
    _____ 20 |__ 0.96 ,__ 0.95 ,__ 0.95 ,__ 0.94 ,__ 0.93 ,__ 0.91
    _____ 25 |__ 0.95 ,__ 0.94 ,__ 0.94 ,__ 0.93 ,__ 0.91 ,__ 0.89
    _____ 30 |__ 0.94 ,__ 0.93 ,__ 0.93 ,__ 0.92 ,__ 0.90 ,__ 0.87
    _____ 40 |__ 0.92 ,__ 0.91 ,__ 0.91 ,__ 0.89 ,__ 0.87 ,__ 0.83
    _____ 50 |__ 0.90 ,__ 0.89 ,__ 0.89 ,__ 0.87 ,__ 0.84 ,__ 0.80
    _____ 60 |__ 0.88 ,__ 0.87 ,__ 0.87 ,__ 0.85 ,__ 0.82 ,__ 0.77
    _____ 70 |__ 0.86 ,__ 0.85 ,__ 0.85 ,__ 0.83 ,__ 0.79 ,__ 0.75
    _____ 80 |__ 0.84 ,__ 0.83 ,__ 0.83 ,__ 0.81 ,__ 0.77 ,__ 0.72
    _____ 90 |__ 0.82 ,__ 0.81 ,__ 0.82 ,__ 0.79 ,__ 0.75 ,__ 0.70
    ____ 100 |__ 0.81 ,__ 0.79 ,__ 0.80 ,__ 0.77 ,__ 0.73 ,__ 0.68
    ____ 120 |__ 0.77 ,__ 0.76 ,__ 0.77 ,__ 0.74 ,__ 0.70 ,__ 0.68
    ____ 150 |__ 0.73 ,__ 0.72 ,__ 0.73 ,__ 0.70 ,__ 0.68 ,__ 0.68
    ____ 200 |__ 0.66 ,__ 0.65 ,__ 0.68 ,__ 0.68 ,__ 0.68 ,__ 0.68
    ____ 250 |__ 0.64 ,__ 0.65 ,__ 0.68 ,__ 0.68 ,__ 0.68 ,__ 0.68
    ___ 1000 |__ 0.64 ,__ 0.65 ,__ 0.68 ,__ 0.68 ,__ 0.68 ,__ 0.68

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ operational P0 / P
    _ _ _ _ _|___
    _____ 15 |__ 1.03 ,__ 1.04 ,__ 1.04 ,__ 1.05 ,__ 1.06 ,__ 1.08
    _____ 20 |__ 1.05 ,__ 1.05 ,__ 1.05 ,__ 1.06 ,__ 1.08 ,__ 1.10
    _____ 25 |__ 1.06 ,__ 1.06 ,__ 1.06 ,__ 1.08 ,__ 1.09 ,__ 1.13
    _____ 30 |__ 1.07 ,__ 1.08 ,__ 1.08 ,__ 1.09 ,__ 1.11 ,__ 1.15
    _____ 40 |__ 1.09 ,__ 1.10 ,__ 1.10 ,__ 1.12 ,__ 1.15 ,__ 1.20
    _____ 50 |__ 1.12 ,__ 1.13 ,__ 1.13 ,__ 1.15 ,__ 1.19 ,__ 1.25
    _____ 60 |__ 1.14 ,__ 1.15 ,__ 1.15 ,__ 1.18 ,__ 1.22 ,__ 1.30
    _____ 70 |__ 1.17 ,__ 1.18 ,__ 1.17 ,__ 1.21 ,__ 1.26 ,__ 1.34
    _____ 80 |__ 1.19 ,__ 1.21 ,__ 1.20 ,__ 1.24 ,__ 1.29 ,__ 1.39
    _____ 90 |__ 1.21 ,__ 1.23 ,__ 1.22 ,__ 1.27 ,__ 1.33 ,__ 1.43
    ____ 100 |__ 1.24 ,__ 1.26 ,__ 1.25 ,__ 1.29 ,__ 1.36 ,__ 1.46
    ____ 120 |__ 1.29 ,__ 1.32 ,__ 1.29 ,__ 1.35 ,__ 1.43 ,__ 1.46
    ____ 150 |__ 1.37 ,__ 1.40 ,__ 1.36 ,__ 1.43 ,__ 1.46 ,__ 1.46
    ____ 200 |__ 1.51 ,__ 1.53 ,__ 1.46 ,__ 1.46 ,__ 1.46 ,__ 1.46
    ____ 250 |__ 1.57 ,__ 1.53 ,__ 1.46 ,__ 1.46 ,__ 1.46 ,__ 1.46
    ___ 1000 |__ 1.57 ,__ 1.53 ,__ 1.46 ,__ 1.46 ,__ 1.46 ,__ 1.46

    ___________________________________________

    EXPONENTIAL GROWTH with Retirement at U

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | P/N , [W / (W/yr)] = years _____ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ ______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 | 133.81 , 107.20 ,_ 85.97 ,_ 71.55 ,_ 57.14 ,_ 42.73 |_ 0.0 |
    ____ 0.1 | 122.44 ,_ 99.40 ,_ 80.40 ,_ 67.67 ,_ 54.64 ,_ 41.32 |_ 0.1 | 2303.7
    ____ 0.2 | 112.48 ,_ 92.45 ,_ 75.41 ,_ 64.11 ,_ 52.32 ,_ 39.99 |_ 0.2 | 1152.4
    ____ 0.5 |_ 89.10 ,_ 75.63 ,_ 63.14 ,_ 55.11 ,_ 46.23 ,_ 36.38 |_ 0.5 |_ 461.7
    ____ 1.0 |_ 64.41 ,_ 56.90 ,_ 49.05 ,_ 44.21 ,_ 38.43 ,_ 31.46 |_ 1.0 |_ 231.4
    ____ 1.5 |_ 49.64 ,_ 45.05 ,_ 39.81 ,_ 36.66 ,_ 32.69 ,_ 27.60 |_ 1.5 |_ 154.7
    ____ 2.0 |_ 40.13 ,_ 37.10 ,_ 33.41 ,_ 31.21 ,_ 28.35 ,_ 24.51 |_ 2.0 |_ 116.3
    ____ 3.0 |_ 28.91 ,_ 27.32 ,_ 25.24 ,_ 24.00 ,_ 22.32 ,_ 19.95 |_ 3.0 |__ 77.9
    ____ 4.0 |_ 22.61 ,_ 21.62 ,_ 20.29 ,_ 19.49 ,_ 18.39 ,_ 16.78 |_ 4.0 |__ 58.7
    ____ 5.0 |_ 18.59 ,_ 17.92 ,_ 16.99 ,_ 16.43 ,_ 15.65 ,_ 14.48 |_ 5.0 |__ 47.2
    ____ 6.0 |_ 15.80 ,_ 15.32 ,_ 14.64 ,_ 14.22 ,_ 13.63 ,_ 12.74 |_ 6.0 |__ 39.5
    ____ 7.0 |_ 13.76 ,_ 13.39 ,_ 12.87 ,_ 12.54 ,_ 12.08 ,_ 11.38 |_ 7.0 |__ 34.0
    ____ 8.0 |_ 12.20 ,_ 11.91 ,_ 11.49 ,_ 11.23 ,_ 10.86 ,_ 10.29 |_ 8.0 |__ 29.9
    ____ 9.0 |_ 10.97 ,_ 10.73 ,_ 10.39 ,_ 10.18 ,__ 9.87 ,__ 9.40 |_ 9.0 |__ 26.7
    ___ 10.0 |__ 9.97 ,__ 9.77 ,__ 9.49 ,__ 9.31 ,__ 9.06 ,__ 8.66 | 10.0 |__ 24.2
    ___ 15.0 |__ 6.91 ,__ 6.81 ,__ 6.68 ,__ 6.59 ,__ 6.46 ,__ 6.25 | 15.0 |__ 16.5
    ___ 20.0 |__ 5.34 ,__ 5.28 ,__ 5.20 ,__ 5.14 ,__ 5.06 ,__ 4.94 | 20.0 |__ 12.6
    ___ 30.0 |__ 3.74 ,__ 3.71 ,__ 3.67 ,__ 3.64 ,__ 3.60 ,__ 3.54 | 30.0 |___ 8.8

    U, years : 221.61 , 199.10 , 198.50 , 165.17 , 131.83 ,_ 98.50
    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | operational P0 / P _____ _ _ _ _ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ ______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 |__ 1.57 ,__ 1.53 ,__ 1.46 ,__ 1.46 ,__ 1.46 ,__ 1.46 |_ 0.0 |
    ____ 0.1 |__ 1.54 ,__ 1.51 ,__ 1.44 ,__ 1.45 ,__ 1.45 ,__ 1.45 |_ 0.1 | 2303.7
    ____ 0.2 |__ 1.51 ,__ 1.48 ,__ 1.42 ,__ 1.43 ,__ 1.43 ,__ 1.44 |_ 0.2 | 1152.4
    ____ 0.5 |__ 1.44 ,__ 1.42 ,__ 1.37 ,__ 1.38 ,__ 1.40 ,__ 1.41 |_ 0.5 |_ 461.7
    ____ 1.0 |__ 1.34 ,__ 1.33 ,__ 1.29 ,__ 1.32 ,__ 1.34 ,__ 1.37 |_ 1.0 |_ 231.4
    ____ 1.5 |__ 1.27 ,__ 1.27 ,__ 1.24 ,__ 1.26 ,__ 1.29 ,__ 1.33 |_ 1.5 |_ 154.7
    ____ 2.0 |__ 1.21 ,__ 1.22 ,__ 1.20 ,__ 1.22 ,__ 1.26 ,__ 1.29 |_ 2.0 |_ 116.3
    ____ 3.0 |__ 1.15 ,__ 1.16 ,__ 1.14 ,__ 1.17 ,__ 1.20 ,__ 1.24 |_ 3.0 |__ 77.9
    ____ 4.0 |__ 1.11 ,__ 1.12 ,__ 1.11 ,__ 1.13 ,__ 1.16 ,__ 1.20 |_ 4.0 |__ 58.7
    ____ 5.0 |__ 1.09 ,__ 1.10 ,__ 1.09 ,__ 1.11 ,__ 1.13 ,__ 1.17 |_ 5.0 |__ 47.2
    ____ 6.0 |__ 1.08 ,__ 1.08 ,__ 1.08 ,__ 1.09 ,__ 1.12 ,__ 1.15 |_ 6.0 |__ 39.5
    ____ 7.0 |__ 1.07 ,__ 1.07 ,__ 1.07 ,__ 1.08 ,__ 1.10 ,__ 1.13 |_ 7.0 |__ 34.0
    ____ 8.0 |__ 1.06 ,__ 1.06 ,__ 1.06 ,__ 1.07 ,__ 1.09 ,__ 1.12 |_ 8.0 |__ 29.9
    ____ 9.0 |__ 1.05 ,__ 1.06 ,__ 1.06 ,__ 1.07 ,__ 1.08 ,__ 1.11 |_ 9.0 |__ 26.7
    ___ 10.0 |__ 1.05 ,__ 1.05 ,__ 1.05 ,__ 1.06 ,__ 1.07 ,__ 1.10 | 10.0 |__ 24.2
    ___ 15.0 |__ 1.03 ,__ 1.04 ,__ 1.03 ,__ 1.04 ,__ 1.05 ,__ 1.07 | 15.0 |__ 16.5
    ___ 20.0 |__ 1.02 ,__ 1.03 ,__ 1.03 ,__ 1.03 ,__ 1.04 ,__ 1.05 | 20.0 |__ 12.6
    ___ 30.0 |__ 1.02 ,__ 1.02 ,__ 1.02 ,__ 1.02 ,__ 1.03 ,__ 1.04 | 30.0 |___ 8.8

    ___________________________________________

    EXPONENTIAL GROWTH, no retirement at a set age

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | P/N , [W / (W/yr)] = years _____ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ ______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 | 199.50 , 142.36 ,_ 99.50 ,_ 82.83 ,_ 66.17 ,_ 49.50 |_ 0.0 |
    ____ 0.1 | 166.33 , 124.62 ,_ 90.50 ,_ 76.50 ,_ 62.06 ,_ 47.16 |_ 0.1 | 2303.7
    ____ 0.2 | 142.64 , 110.83 ,_ 83.00 ,_ 71.07 ,_ 58.44 ,_ 45.04 |_ 0.2 | 1152.4
    ____ 0.5 | 100.00 ,_ 83.25 ,_ 66.50 ,_ 58.62 ,_ 49.75 ,_ 39.70 |_ 0.5 |_ 461.7
    ____ 1.0 |_ 66.83 ,_ 58.91 ,_ 50.00 ,_ 45.41 ,_ 39.90 ,_ 33.16 |_ 1.0 |_ 231.4
    ____ 1.5 |_ 50.25 ,_ 45.63 ,_ 40.10 ,_ 37.09 ,_ 33.33 ,_ 28.50 |_ 1.5 |_ 154.7
    ____ 2.0 |_ 40.30 ,_ 37.28 ,_ 33.50 ,_ 31.37 ,_ 28.64 ,_ 25.00 |_ 2.0 |_ 116.3
    ____ 3.0 |_ 28.93 ,_ 27.33 ,_ 25.25 ,_ 24.02 ,_ 22.39 ,_ 20.10 |_ 3.0 |__ 77.9
    ____ 4.0 |_ 22.61 ,_ 21.62 ,_ 20.30 ,_ 19.50 ,_ 18.40 ,_ 16.83 |_ 4.0 |__ 58.7
    ____ 5.0 |_ 18.59 ,_ 17.92 ,_ 17.00 ,_ 16.43 ,_ 15.65 ,_ 14.49 |_ 5.0 |__ 47.2
    ____ 6.0 |_ 15.80 ,_ 15.32 ,_ 14.64 ,_ 14.22 ,_ 13.63 ,_ 12.74 |_ 6.0 |__ 39.5
    ____ 7.0 |_ 13.76 ,_ 13.39 ,_ 12.87 ,_ 12.54 ,_ 12.08 ,_ 11.38 |_ 7.0 |__ 34.0
    ____ 8.0 |_ 12.20 ,_ 11.91 ,_ 11.49 ,_ 11.23 ,_ 10.86 ,_ 10.29 |_ 8.0 |__ 29.9
    ____ 9.0 |_ 10.97 ,_ 10.73 ,_ 10.39 ,_ 10.18 ,__ 9.87 ,__ 9.40 |_ 9.0 |__ 26.7
    ___ 10.0 |__ 9.97 ,__ 9.77 ,__ 9.49 ,__ 9.31 ,__ 9.06 ,__ 8.66 | 10.0 |__ 24.2
    ___ 15.0 |__ 6.91 ,__ 6.81 ,__ 6.68 ,__ 6.59 ,__ 6.46 ,__ 6.25 | 15.0 |__ 16.5
    ___ 20.0 |__ 5.34 ,__ 5.28 ,__ 5.20 ,__ 5.14 ,__ 5.06 ,__ 4.94 | 20.0 |__ 12.6
    ___ 30.0 |__ 3.74 ,__ 3.71 ,__ 3.67 ,__ 3.64 ,__ 3.60 ,__ 3.54 | 30.0 |___ 8.8

    _ -hs (%):__ 0.05 ,__ 0.20 ,__ 0.50 ,__ 0.60 ,__ 0.75 ,__ 1.00
    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    __ s (%) | operational P0 / P _____ _ _ _ _ _ _ _ _ _ _ _ _ _ _| s (%)| time (yrs) to grow
    _ _ _ _ _|___ ______ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __| ____ |_ by factor of 10
    ____ 0.0 |_ 10.02 ,__ 3.51 ,__ 2.01 ,__ 2.01 ,__ 2.01 ,__ 2.01 |_ 0.0 |
    ____ 0.1 |__ 4.01 ,__ 2.67 ,__ 1.84 ,__ 1.86 ,__ 1.89 ,__ 1.92 |_ 0.1 | 2303.7
    ____ 0.2 |__ 2.81 ,__ 2.26 ,__ 1.72 ,__ 1.76 ,__ 1.80 ,__ 1.84 |_ 0.2 | 1152.4
    ____ 0.5 |__ 1.82 ,__ 1.72 ,__ 1.50 ,__ 1.55 ,__ 1.61 ,__ 1.68 |_ 0.5 |_ 461.7
    ____ 1.0 |__ 1.43 ,__ 1.42 ,__ 1.34 ,__ 1.38 ,__ 1.43 ,__ 1.51 |_ 1.0 |_ 231.4
    ____ 1.5 |__ 1.29 ,__ 1.30 ,__ 1.25 ,__ 1.29 ,__ 1.34 ,__ 1.41 |_ 1.5 |_ 154.7
    ____ 2.0 |__ 1.22 ,__ 1.23 ,__ 1.20 ,__ 1.23 ,__ 1.28 ,__ 1.34 |_ 2.0 |_ 116.3
    ____ 3.0 |__ 1.15 ,__ 1.16 ,__ 1.15 ,__ 1.17 ,__ 1.20 ,__ 1.26 |_ 3.0 |__ 77.9
    ____ 4.0 |__ 1.11 ,__ 1.12 ,__ 1.11 ,__ 1.13 ,__ 1.16 ,__ 1.21 |_ 4.0 |__ 58.7
    ____ 5.0 |__ 1.09 ,__ 1.10 ,__ 1.09 ,__ 1.11 ,__ 1.13 ,__ 1.17 |_ 5.0 |__ 47.2
    ____ 6.0 |__ 1.08 ,__ 1.08 ,__ 1.08 ,__ 1.09 ,__ 1.12 ,__ 1.15 |_ 6.0 |__ 39.5
    ____ 7.0 |__ 1.07 ,__ 1.07 ,__ 1.07 ,__ 1.08 ,__ 1.10 ,__ 1.13 |_ 7.0 |__ 34.0
    ____ 8.0 |__ 1.06 ,__ 1.06 ,__ 1.06 ,__ 1.07 ,__ 1.09 ,__ 1.12 |_ 8.0 |__ 29.9
    ____ 9.0 |__ 1.05 ,__ 1.06 ,__ 1.06 ,__ 1.07 ,__ 1.08 ,__ 1.11 |_ 9.0 |__ 26.7
    ___ 10.0 |__ 1.05 ,__ 1.05 ,__ 1.05 ,__ 1.06 ,__ 1.07 ,__ 1.10 | 10.0 |__ 24.2
    ___ 15.0 |__ 1.03 ,__ 1.04 ,__ 1.03 ,__ 1.04 ,__ 1.05 ,__ 1.07 | 15.0 |__ 16.5
    ___ 20.0 |__ 1.02 ,__ 1.03 ,__ 1.03 ,__ 1.03 ,__ 1.04 ,__ 1.05 | 20.0 |__ 12.6
    ___ 30.0 |__ 1.02 ,__ 1.02 ,__ 1.02 ,__ 1.02 ,__ 1.03 ,__ 1.04 | 30.0 |___ 8.8

  6. 306
    Patrick 027 says:

    “Some combinations that result in $10 / average W

    (assuming high fill factors or concentration of sunlight into time intervals – more generally, that the average efficiency of conversion is not much lower than the rated efficiency of conversion ):”…

    To clarify: Those combinations assume the average efficiency is close to the rated efficiency at 1000 W/m2 insolation (a standard full sun, presumably mostly direct solar radiation) AT THE TIME of purchase or installation – when the collector is new.

  7. 307
    Patrick 027 says:

    The last row of one of the tables was erroneously zero: Correction:

    ONE TIME INSTALLMENT

    __ -h (%):__ 0.50 ,__ 0.70 ,__ 1.00 ,__ 1.20 ,__ 1.50 ,__ 2.00
    _ _ _ _ _|____________________________________________________
    t, years |_ Average ( P/ installed P0 ) from installation to time t since installation
    _ _ _ _ _|___

    ___ 1000 |__ 0.20 ,__ 0.14 ,__ 0.10 ,__ 0.08 ,__ 0.07 ,__ 0.05

    __________________________________________________

    I also included hs in some tables when the table values did not directly depend on it, and only depended on it indirectly through U (U was determined from he, which was determined from the combination of h and hs values).

    This applies to these tables:

    m0 for:

    1. CONSTANT N (with and without debt) (note that U only affects the calculation for t larger than U)

    2. EXPONENTIAL GROWTH with Retirement at U

    and

    P/N for:

    1. CONSTANT N (note that U only affects the calculation for t larger than U)

    2. EXPONENTIAL GROWTH with Retirement at U

    In general, m0 only depends on hs through U, and when it depends on U. The same is true of P/N. P0/N depends on hs, so P0/P depends on h and hs.

  8. 308
    Douglas Wise says:

    re #1242 John Reisman

    You suggest that James, who is concerned for species other than his own and who believes that we have a severe problem of human overpopulation, should contribute to its solution by topping himself.

    I fear that such a single selfless act would do little good unless it served as encouragement for a further 2 to 4 billion others to volunteer in like manner. The rest of us might then thrive. However, we’ll probably get the same or a worse outcome with BAU without the painful necessity of having to make the choice of becoming volunteers, not that this will eliminate pain in any way.

    Before setting the high moral tone for the rest of us, I would invite you to contemplate the following thought experiments and then apply your exemplary moral standards to them.

    1) You are on a lifeboat with 9 others. You have no means of feeding yourself. You know that it is 99.9% probable that you won’t reach landfall unless you eat one or more of your fellow passengers. What do you do?
    a) All agree to starve.
    b) Volunteer yourself as the first meal.
    c) Gang up with a few others to kill the remainder as soon as possible before they come up with the same idea.
    d) Democratically (or otherwise) work out a pecking order to establish the rank in which you become the consumed rather than the consumer, eating, may it be said, in a fruglal but sustainable manner on humane grounds and thus minimising the death toll.

    2) Same lifeboat and personnel. This time you know that the only landfall is sterile and won’t sustain you. However, you have with you some seed corn and a few chickens which could potentially save you when you reach land. From your comments about James, I gather that you think he’d eat people and leave the non human food resource to ensure the survival of a few. You seem to deem this immoral and so I gather you’d head straight for the wheat and chickens so dooming everyone by failing to take difficult choices because of moral squeamishness. On reflection, I probably misjudge you. You’d take the easy option and eat the chickens only and argue for a vegetarian future, despite problems of future pernicious anaemia.

    I hope things don’t come to this but it seems likely that they will unless we get our act together very quickly indeed.

  9. 309
    Mark says:

    Douglas, 308, no, I’m concerned that James is making up anything he can to keep the conclusion that he wants to see maintained: Nuclear Power is teh bomb! Uh, sorry, The Best Thing Since Sliced Bread.

    Oracle seems to agree: troller woosnam