Extracción ar dehe mextha ya dätä nt'ot'e ir nge ya ultrasonidos nts'edi
Water extraction of botanical compounds (e.g., cold or hot water extraction, pressurized water extraction and subcritical water extraction) can be efficiently improved by ultrasonication. The ultrasound-assisted water extraction not only gives higher yields and reduces processing time, but also results in lower energy consumption, milder extraction conditions and high-quality extracts when compared to conventional extraction techniques. Ultrasonic water extraction is successfully used for the extraction of numerous plant-derived compounds including alkaloids, flavonoids, glycosides, phenolic compounds and polysaccharides.
Ultrasonic Water Extraction of Bioactive Compounds
Water is the most polar solvent, which makes it a great solvent for polar compounds. Due to is non-toxic and environmental-friendly nature, water would be the ideal solvent for any botanical extract. However, less-polar and non-polar components are poorly or not at all dissolving in water. Additionally, without any mass transfer promotion, the extraction process in water would be incredibly slow and thereby uneconomical. High-intensity, low-frequency ultrasound is a very efficient extraction technique, which provides intense mixing and mass transfer. Therefore, ultrasonic extraction is well known to provide significant advantages over conventional extraction methods. These advantages include higher yields, rapid processing, quick rapid batch turnovers as well as continuous inline extraction, the use of green solvents, mild extraction conditions, which preserve the extract compounds, safety in operation, and easy scalability to large throughputs for commercial production. (cf. Zabot et al., 2021)
Hot Water Extraction Improved by Ultrasonication
The parameters that determine the extraction of botanicals during water extraction are temperature, time, pressure, and surface area of plant material. A hot water extract can be prepared during a relatively short duration due to the high temperature of water.
Ár njäts'i: Yield and extraction rate can be significantly enhanced when ultrasonic stirring is applied. Hot water alone has only a limited capability to break cell structures and high temperatures often damage or destroy heat-labile compounds, so that the extract quality suffers. When ultrasonic extraction is combined with hot water extraction, the temperature can be drastically reduced (e.g. from 100°C to 50°C), which prevents thermal degradation of the extracted botanical ingredients, increases the total yield, and saves energy. Ultrasonic cavitation is the principle behind the ultrasonic extraction phenomenon. Ultrasonic (or acoustic) cavitation are purely mechanical forces, which break cell walls, release the target compounds and improve the mass transfer between the cell interior and the water (solvent). Thus, ultrasonic water extraction provides excellent extraction results.
Cold Water Extraction Improved by Ultrasonication
Cold water extraction (cold water infusion) is significantly more inefficient, since the use hot water is avoided. Cold or room temperature water doesn’t extract botanical compounds very well, since the cold water is soaked really slowly into the plant material and mass transfer is almost negligible. The advantage of cold water extraction lies in the avoidance of any temperature rise thereby preventing the thermal degradation of heat-sensitive compounds. However, the very poor extraction dynamics make conventional cold water extraction impracticable for commercial production. That’s why cold water infusion is almost exclusively used in experimental stage due to is slowness and inefficiency.
Ár njäts'i: With the introduction of ultrasonication into cold water extraction, the slowness and inefficiency of cold water soaking can be easily overcome. The ultrasonically-intensified cold water extraction allows to maintain cold extraction temperatures, whilst coupling intense shear forces into the solid-liquid medium. As result of the ultrasonic extraction mechanism, cell walls are opened and the botanical compounds are rapidly released into the water. Ultrasonic cold water extraction and infusion turns the cold soaking into a highly efficacious process giving high yields, high quality extracts within a short extraction time.
Pressurized Water Extraction combined with Ultrasonication
Ultrasonic extraction is characterized by micro-mixing, which through vibrations, promotes greater diffusion of the solvent into the particle and from the particle’s interior to the surface, intensifying the mass transfer. Additionally, ultrasonication reduces the particle size of the cellular material, which leads to improved effects of ultrasonically-assisted pressurized liquid extraction. Smaller particles of approx. 0.68 mm show higher yields than larger particles (approx. 1.05 mm) as a higher surface area allows for significantly increased mass transfer and thereby improved extraction yields. (cf. Zabot et al., 2021)
- Rendimiento mäs xi ngu
- Extracción mextha velocidad
- Extractos mextha ar hño
- Mild, non-thermal procedure
- Disolventes verdes
- Rentable
- Operación hei ne segura
- Bajos costos inversión ne operación
- Operación 24 yá 7 jár 'be̲fi hñei
- Nt'ot'e xí ne respetuoso ko ar nt'uni mbo jar ximha̲i
Efficacious Pressurized Cold Water Extraction with Power-Ultrasound
Under high pressure, the penetration of cold water into plant tissues is facilitated and water-soluble phytochemicals are dissolved without causing thermal decomposition. The high-pressure cold water extraction method can be coupled with ultrasound for an improved isolation of polar and non-polar botanical ingredients. Water as a nontoxic, cheap, and environmental-friendly solvent is an attractive alternative to organic solvent, especially when it comes to the production of plant-derived food, therapeutics, and dietary supplements.
For an ultrasonically-intensified pressurized cold water extraction, an ultrasonic probe (sonotrode) is integrated into the the extraction tank or flow cell. Tank or flow cell are normally pressurized with pressures between 5 and 100 barg depending on the targeted extract compounds. Hielscher Ultrasonics supplies even customized industrial ultrasonic reactors and flow cell, which can pressurized up to 300barg allowing to set the optimal pressure of your extraction process.
Supercritical Water Extraction Improved by Sonication
An ultrasonically enhanced subcritical water extraction is another synergetic technique, where power ultrasound improves the mass transfer between solid and liquid. Subcritical-water extraction (SWE) – also known as pressurized hot water extraction or superheated water extraction – is a less commonly used technique for the extraction of botanical compounds with a lower polarity. In subcritical-water extraction, water in its supercritical state is used as solvent.
What is subcritical water and why is subcritical water a good solvent for extraction of less-polar plant compounds? “Water possesses many thermodynamic properties greatly influenced by temperature and pressure. Depending on conditions, its physical state (solid, liquid, or gas), thermal behavior, density, or viscosity can be modified. By increasing temperature and pressure over a point known as critical point (defined at 221 bar and 374 °C), water can attain the supercritical state. At subcritical conditions, corresponding to temperatures between 100°C and critical temperature (374°C) and pressure between 1 bar and critical pressure (221 bar) in order to avoid vaporization, water polarity decreases; it makes water a better solvent for the extraction of various organic bioactive compounds.” (Li and Chemat, 2019)
When ultrasonics is combined with subcritical water extraction, extraction efficiency can be improved by increasing extract yield and reducing extraction time. For optimal results, the pressure in the closed pressurized batch reactor or flow cell reactor should reach at least twice as high as the vapour pressure of water. (You can find a table of the vapour pressure of water at the end of this page.)
Huang et al. (2010) investigated the extraction effects of low-frequency, high-power ultrasound in combination with subcritical water extraction. An ultrasonic probe is therefore coupled into the kettle of subcritical water extraction device to extract volatile oil from Lithospermum erythrorhizon. The results showed that the ultrasound-assisted enhancement effect of 20 KHz was better than that of 36 KHz and increased with output power (from 0 to 250 W). The subcritical water extraction yield increased from 1.87% to 2.39% via ultrasonic oscillation (250 W, 20 KHz) at a temperature of 160°C and a pressure of 5 MPa during a 25-minute extraction procedure. Ultrasonication could improve not only the extraction yield, but also the extraction rate thereby saving time.
Ultrasonically-assisted subcritical water extraction can be run at lower pressures (e.g., 5barg) than conventional subcritical water extraction (e.g., 10MPa), which saves energy-costs and makes the extraction procedure safer.
Ya ventajas ar extracción botánica ultrasónica
Both, scientific research and industrial implementation demonstrate that ultrasound-assisted extraction is a reliable and easy-to-operate technique, which requires no technical background or intensive training. Very high extraction efficiency, high yields, low operational costs, as well as low investment costs (especially when compared to other techniques such as CO2 extractors) and low energy costs are the main advantages of probe-type ultrasonic extractors.
Further benefits, which turn the ultrasonic extraction technology into the preferred method, are high quality extracts due to low extraction temperatures, reliable outcomes (repeatability / reproducibility), completely linear scalability to any production level as well as low maintenance.
„Other advantages linked with the use of ultrasonic probe-type extraction are easy handling of extract, rapid execution, no residues, high yield, eco-friendly, enhanced quality and prevention of extract degradation.“
(cf. Chemat and Khan, 2011)
High Performance Ultrasonicators for Water Extraction
Hielscher Ultrasonics extractors are well established in the field of botanical extraction, no matter what solvent is used. Extract producers – both, smaller, exclusive niche extract manufacturers as well as large-scale mass producers – find in Hielscher‘ broad equipment portfolio the ideal ultrasonic extraction equipment for their production requirements. Batch as well as continuous inline process setups are readily available and can be shipped off the shelf. Suitable to work with any solvent, ultrasonic extraction can be flexibly applied for any plant material extraction. Using water as solvents allows to produce organic-certified extracts without the use of highly expensive “organic” ethanol. (Of course, the plant material must be organically grown order to produce an organic water extract).
High Efficiency Extraction with Hielscher Ultrasonics
Hielscher Ultrasonic extractors efficiently disrupt plant cells, increase the surface area of the plant material for solvent penetration, and mass transfer for the release of phytochemicals (secondary metabolites). Designed with regards to user-friendliness, Hielscher extractors are quickly installed and can be safe and intuitively operated.
Cumpliendo ko ya mäs altos estándares hño – Diseñado & Fabricado nu Alemäña
Sofisticado ar hardware ne ar software inteligente ya ultrasonidos Hielscher gi 'bu̲hu̲ diseñados pa garantizar 'ra resultados fiables extracción ya ultrasonidos ár materia prima botánica ko resultados reproducibles ne 'nar funcionamiento hei ne pädi xi hño. Ar robustez, ar fiabilidad, ar funcionamiento 24 yá 7 bí plena ar carga ne ar sencillez manejo ndezu̲ ar punto ar thandi ya ar pe̲fi ya ma'ra factores ar hño mi o̲t'e ne ya ultrasonidos Hielscher 'bu̲hu̲ favorables.
Ya extractores ultrasónicos Hielscher ar utilizan jar nga̲tho ar ximha̲i jar extracción fitoquímica mextha ar hño. Ya extractores ultrasónicos ar Hielscher, nä'ä xi demostrado producir compuestos botánicos mextha ar hño, hingi ho̲ntho ya utilizados ya t'olo artesanos extractos mfädi ne boutique, pe ge ga̲tho jar producción industrial extractos, suplementos nutricionales ne terapéuticos ampliamente da 'mui jar jár ta̲i. Jamädi robusto ár hardware ne da software ár inteligente, ya procesadores ultrasónicos Hielscher xi 'ye̲ ar ne monitorizar ar hingi hembi da.
Protocolización automática datos
Pa da tsoni ko ya estándares producción nts'i, suplementos nutricionales ne productos terapéuticos, ya procesos producción tsa da monitoreados ne Nthuts'i jar detalle. Ya dispositivos ultrasónicos digitales ar Hielscher Ultrasonics pede yá 'bede ko protocolización automática ar datos. Jamädi xí función inteligente, nga̲tho ya parámetros mahyoni ja ar proceso, komongu ar energía ultrasónica (energía Nxoge ne ya neta), ar mpat'i, ar presión ne ar pa ar almacenan automáticamente 'na jar tarheta SD incorporada en cuanto bí enciende ar dispositivo. Ar monitorización ar procesos ne ar registro datos mahyoni pa ar estandarización continua ya procesos ne ya ar producto. Ar acceder ja ya datos ar proceso Nthuts'i automáticamente, to da hnu ya ejecuciones ar sonicación bí thogi ne evaluar ar nt'uni.
Gi característica ar hei ar zu̲di ge ar control remoto navegador HMUNTS'UJE sistemas ultrasónicos digitales. A través de ar control remoto ar navegador, to da du'mi, detener, ajustar ne supervisar ár procesador ultrasónico dets'e remota ndezu̲ 'na lugar.
Want to learn more about the advantages of ultrasonic water extraction from plant materials? Contact us now to discuss your botanical extract manufacturing process! Our well-experienced staff will be glad to share more information about ultrasonic extraction, our ultrasonic systems and pricing!
Xtí tabla bí xta ar 'nar indicación ya mfeni ya procesamiento aproximada ar HMUNTS'UJE ultrasonidos:
Volumen lote | Gasto | Dispositivos recomendados |
---|---|---|
Ar 1 jar 500 ml | Ar 10 200 ml yá min | UP100H |
Ar 10 da 2000 ml | Ar 20 400 ml yá min | UP200Ht, UP400St |
0.1 da 20L | 0.2 4 L yá min | UIP2000hdT |
Ar 10 da 100L | Ar 2 10 l yá min | UIP4000hdT |
n.d. | Ar 10 100 L yá min | UIP16000 |
n.d. | Mar dätä | Racimo ar UIP16000 |
Contactar ga! Yá preguntar ga!
Technical Information About Ultrasonic Water Extraction
Conventional extraction methods such as maceration, infusion, percolation, decoction, reflux extraction, steam distillation, sublimation and pressing are commonly used in the extraction of medicinal compounds from plants. The disadvantages of these methods include time-consuming process, poor purity and low efficiency.
Process Parameters influencing Ultrasonic Extraction
Ultrasonically-assisted extraction is known for its unique features and advantages, which make sonication the superior extraction technique when compared to conventional extraction methods of botanical compounds. A major advantage of ultrasound-assisted extraction lies in the precise adaptability of ultrasonic processing factors (such as amplitude, time, temperature, pressure), which allows to tune the ultrasonic process optimally to the target compound. Each plant material has ideal extraction parameters, under which best yield, quality and extraction rate are achieved. The ultrasonic extraction process allows to adapt these optimal extraction conditions perfectly.
Amplitud ultrasónica
The amplitude is the vibrational displacement of the ultrasonic probe (sonotrode). The higher the amplitude, the more intense the vibration and cavitation in the sonicated liquid. Hielscher Ultrasonics is spezialized in high-performance probe-type ultrasonicators, which can supply precisely adjustable amplitudes. Customized probes, which can deliver up to 200µm in continuous 24/7 operation are readily available off the shelf. For even higher amplitudes, customized ultrasonic sonotrodes can be easily manufactured, too.
The amplitude is one – if not the single-most – important parameter for efficient plant extraction. High amplitudes create the required forces to break up cell walls and to release the intracellular material. Thereby, high-performance ultrasonication becomes so efficacious in botanical extraction.
Time / Duration Of Ultrasonic Treatment
Ultrasound-assisted extraction is usually much shorter than traditional methods, since sonication releases the botanical compounds at significantly higher extraction rates. Ultrasonication allows for shorter extraction procedures, which preserves the extracted compounds against over-processing. Shorter processing due to ultrasound means higher throughput and higher extract quality.
Pulsed Ultrasonic Treatment
Ultrasonic pulsation is a treatment mode, where the ultrasound treatment is discontinued by defined pause cycles (e.g. 50% duty cycle: 30 sec. ON, 30 sec. OFF; 100% duty cyle: continuous sonication without pauses) The duty cycle of ultrasound (also known as pulse mode or ultrasonic pulsation cycles) refers to the percentage of time during which ultrasound is coupled into the medium (pulse duration) over one pulse period. For instance, a 50% cycle mode would be 30 sec. ON, 30 sec. OFF. During the pause cycle of a duty cycle, the sonicated liquid comes for a defined time (e.g., 30 sec.) back to a undisturbed state, which is good for heat-dissipation in order to maintain a target processing temperature. The duty cycle of sonication is less important duty cycle for extraction efficiency, but is used to maintain a certain process temperature.
Hydrostatic Pressure
Pressure is another very important parameter for ultrasonic processes. Applying hydrostatic pressure to the sonicated medium affects the intensity of cavitation. Under elevated pressure conditions, the intensity of ultrasonic (acoustic) cavitation is augmented. Hielscher Ultrasonics offers various types of ultrasonic batch reactors and flow cells, which can be pressurized for intensified sonication results.
Tsoxpa extracción
Like any mechanical treatment, ultrasonication causes a rise in temperature, which is in accordance to the 2nd law of thermo-dynamics. Nevertheless, ultrasonication is a non-thermal treatment technique, since ultrasound-assisted treatments are based on purely mechanical forces (also called sonomechanical forces). Extraction temperature during ultrasonic extraction can be efficiently controlled and maintained within a certain selected temperature range. All Hielscher digital ultrasonic processors are equipped with a pluggable temperature sensor and a smart software, where a certain temperature range can be set for the process. Whenever this temperature range is exceeded, the ultrasonicator pauses until the temperature is in the selected range again and continues then automatically the sonication procedure. This smart feature of Hielscher ultrasonicators allows for a precisely controllable sonication process and ideal results.
Since the extraction temperature may be different any botanical compounds and plant, temperature is an important factor, which should not be neglected during ultrasonic process optimization. For instance, 80°C was found to be ideal to achieve maximum yield of flavonoids from Sophora flavescens, whilst best results were obtained at 50°C for the extraction of arabinoxylan from wheat bran.
Use Any Solvent for Ultrasonic Extraction
Different botanical compounds have different polarities, which affect their solubility in various solvents. For instance, saponins and polysaccharides are more polar and show therefore good solubility in water, since water is highly polar. Phenolic compounds such as anthocyanins and chlorogenic acid, on the other hand, are quite unpolar and dissolve therefore better a less-polar solvent such as ethanol. Thus, the choice of solvent should be made in accordance to the solubility of targeted compounds in order to obtain high extraction efficiency. For instance, water is a good solvent for the extraction of polar compounds such as psilocybin from mushrooms as well as oligosaccharides, glycosides, and flavanoids; whilst an ethanol-water mixture with and ethanol concentration of 60% (v/v) is suitable for the ultrasonically-assisted extraction of e.g., apigenin, baicalin and luteolin compounds.
Read more about solvents, solvent polarity and the most suitable solvents for ultrasonic extraction!
Water as Extraction Solvent
Water is the most polar solvent and is suitable for the extraction of a wide range of polar compounds. Its major advantages include the capability to dissolve a wide range of substances. Furthermore, it is cheap, nontoxic, safe, and nonflammable. Its disadvantages includes the strong selectivity for polar compounds due to its high polarity. Due to its high boiling point of 100°C, the concentration of the extract (e.g. via distillation or rotor-evaporation) requires a large amount of energy. Furthermore, water is prone to bacterial and mold growth.
Frecuencia ultrasónica
The ultrasonic frequency around 20kHz has been established as most powerful and efficient for botanical extraction. impacts the efficiency of ultrasound-assisted extraction in the extraction of medicinal compounds from plants. In general, the low ultrasonic frequency (i.e., at approx. 20kHz) generates more intense cavitation (sonomechanical effects), which results in higher efficacy of the extraction procedure.
The Plant Material
Plant materials can vary heavily in structure and rigidity of their cells. Depending on the cell wall composition, which may contain cellulose, hemicelluloses, lignin, pectic polysaccharides, proteins, phenolic and non-cellulosic compounds, and water, cell walls can be either sturdy or soft. Different plant types and parts contain different types and amounts of these cell wall components. That’s why each type of plant requires specific processing parameters for optimum extraction outcomes.
As intensity can be precisely tuned, Hielscher ultrasonic extractors can be reliably break soft and hard cell walls. Soft cell walls may need less intense ultrasonication, whilst sturdy cell structures benefit from a more intense treatment.
The raw material for botanical extraction can be freshly harvested (wet) or dried. Ultrasonic extraction is suitable for both fresh/wet as well as dried plants. Particle size of the plant solids is another importnat factor: A high surface area (i.e., small particle size) is beneficial since it provides a large contact area for the ultrasonic cavitational shear forces, resulting in higher efficiency. Therefore, plant material is macerated or ground into small pieces (approx. 3-5mm).
¿Yogo'ä ar extracción ultrasónica ar mäs xi hño ár nt'ot'e?
Eficacia
- Pe̲ts'i ar rendimientos
- Proceso ar extracción rápido – Ja ya nt'ot'e nuya ya t'olo ora
- Extractos mextha ar hño – Extracción za̲tho, hingi térmica
- Green solvents (water, ethanol, glycerin, vegetable oils, NADES etc.)
Simplicidad
- Plug — and — play: configuración ne funcionamiento ja ya nt'ot'e nuya ya t'olo ora
- Mar hñets'i rendimiento: pa ar producción extractos Nar dätä hño escala
- Operación jar 'ñu continua wa ja ya lotes
- Instalación ne puesta da ndu̲i sencillas
- Portátil yá Móvil — Unidades portátiles wa ya construidas dige ar ruedas
- Escalado lineal: agregue ma'na ko ya ultrasónico jar paralelo pa aumentar mfeni
- Supervisión ne control remotos: a través de PC, teléfono inteligente wa ya tableta
- Hingi bí requiere ar supervisión ar proceso: configuración ne nt'eni
- Mar hñets'i rendimiento: diseñado pa 'nar producción continua 24 ya ora ar pa, 7 ya pa ar su̲mänä
- Robustez ne hñets'i'i nja
- Mextha ar hño – diseñado ne construido nu Alemäña
- Carga ne descarga ngut'a entre lotes
- Hei ar limpiar
Ntsuni
- Sencillo ne pädi xi hño ar ejecutar
- Extracción hinda disolventes wa ko base disolventes (dehe, etanol, aceites vegetales, glicerina, etcétera).
- 'Ñotho ar altas ar presiones ne ar temperaturas
- Sistemas ntsa̲ explosiones ko certificación ATEX da 'mui
- Hei ar controlar ('nehe a través de ar mando da mbi)
Bibliografía yá Referencias
- Ping-ping Huang, Ri-fu Yang, Tai-qiu Qiu, Wei Zhang & Chun-mei Li (2010): Ultrasound-Enhanced Subcritical Water Extraction of Volatile Oil from Lithospermum erythrorhizon. Separation Science and Technology, 45:10, 1433-1439.
- Zabot, G. L., Viganó, J., & Silva, E. K. (2021): Low-Frequency Ultrasound Coupled with High-Pressure Technologies: Impact of Hybridized Techniques on the Recovery of Phytochemical Compounds. Molecules, 26(17), 2021. 5117.
- Li, Ying; Chemat, Farid (2019): Plant Based “Green Chemistry 2.0”: Moving from Evolutionary to Revolutionary. Springer Science 2019.
- Petigny L., Périno-Issartier S., Wajsman J., Chemat F. (2013): Batch and Continuous Ultrasound Assisted Extraction of Boldo Leaves (Peumus boldus Mol.). International journal of Molecular Science 14, 2013. 5750-5764.
- Fooladi, Hamed; Mortazavi, Seyyed Ali; Rajaei, Ahmad; Elhami Rad, Amir Hossein; Salar Bashi, Davoud; Savabi Sani Kargar, Samira (2013): Optimize the extraction of phenolic compounds of jujube (Ziziphus Jujube) using ultrasound-assisted extraction method.
- Dogan Kubra, P.K. Akman, F. Tornuk (2019): Improvement of Bioavailability of Sage and Mint by Ultrasonic Extraction. International Journal of Life Sciences and Biotechnology, 2019. 2(2): p.122- 135.
- algas
- Antocianinas
- artemisinina
- Astragalus
- Baggibuti
- melón amargo
- cannabis
- guindillas
- canela
- Citrus fruit peel
- cacao
- kafe
- Cucurmin
- lenteja ar dehe
- saúco
- ajo
- jengibre
- té xí
- lúpulo
- Kratom
- Pasto medicinales
- Silymarin from Milk Thistle
- Ixi ar monje
- champiñones
- Hojas olivo
- granada
- quercetina
- Quillaja
- azafrán
- Stevia
- tabaco
- vainilla
and many more!
Table: Vapour Pressure of Water
Tsoxpa in °C |
Vapour Pressure in mmHg (Torr) |
Vapour Pressure in Hectopascal hPa |
-80 | 0,00041 | 0,00055 |
-75 | 0,000915 | 0,00122 |
-70 | 0,00196 | 0,00261 |
-65 | 0,00405 | 0,0054 |
-60 | 0,008101 | 0,0108 |
-55 | 0,0157 | 0,02093 |
-50 | 0,02952 | 0,03936 |
-45 | 0,05402 | 0,07202 |
-40 | 0,09631 | 0,1284 |
-39,5 | 0,1019 | 0,1359 |
-39 | 0,1078 | 0,1437 |
-38,5 | 0,114 | 0,1520 |
-38 | 0,1206 | 0,1607 |
-37,5 | 0,1274 | 0,1699 |
-37 | 0,1347 | 0,1796 |
-36,5 | 0,1423 | 0,1897 |
-36 | 0,1503 | 0,2004 |
-35,5 | 0,1587 | 0,2116 |
-35 | 0,1676 | 0,2235 |
-34,5 | 0,1769 | 0,2359 |
-34 | 0,1867 | 0,2490 |
-33,5 | 0,197 | 0,2627 |
-33 | 0,2078 | 0,2771 |
-32,5 | 0,2192 | 0,2923 |
-32 | 0,2311 | 0,3082 |
-31,5 | 0,2437 | 0,3249 |
-31 | 0,2568 | 0,3424 |
-30,5 | 0,2706 | 0,3608 |
-30 | 0,2851 | 0,3801 |
-29,5 | 0,3003 | 0,4004 |
-29 | 0,3162 | 0,4216 |
-28,5 | 0,333 | 0,4439 |
-28 | 0,3505 | 0,4673 |
-27,5 | 0,3688 | 0,4918 |
-27 | 0,3881 | 0,5174 |
-26,5 | 0,4083 | 0,5443 |
-26 | 0,4294 | 0,5725 |
-25,5 | 0,4515 | 0,6020 |
-25 | 0,4747 | 0,6329 |
-24,5 | 0,4989 | 0,6652 |
-24 | 0,5243 | 0,6991 |
-23,5 | 0,5509 | 0,7345 |
-23 | 0,5787 | 0,7716 |
-22,5 | 0,6078 | 0,8104 |
-22 | 0,6383 | 0,851 |
-21,5 | 0,6701 | 0,8934 |
-21 | 0,7034 | 0,9377 |
-20,5 | 0,7381 | 0,9841 |
-20 | 0,77451 | 1,0326 |
-19,5 | 0,81251 | 1,0833 |
-19 | 0,85222 | 1,1362 |
-18,5 | 0,89368 | 1,1915 |
-18 | 0,93698 | 1,2492 |
-17,5 | 0,98222 | 1,3095 |
-17 | 1,0295 | 1,3725 |
-16,5 | 1,0787 | 1,4382 |
-16 | 1,1302 | 1,5068 |
-15,5 | 1,1839 | 1,5783 |
-15 | 1,2399 | 1,653 |
-14,5 | 1,2983 | 1,7309 |
-14 | 1,3593 | 1,8122 |
-13,5 | 1,4228 | 1,8969 |
-13 | 1,489 | 1,9852 |
-12,5 | 1,5581 | 2,0773 |
-12 | 1,6300 | 2,1732 |
-11,5 | 1,705 | 2,2732 |
-11 | 1,7832 | 2,3774 |
-10,5 | 1,8646 | 2,4859 |
-10 | 1,9494 | 2,5990 |
-9,5 | 2,0377 | 2,7168 |
-9 | 2,1297 | 2,8394 |
-8,5 | 2,2254 | 2,9670 |
-8 | 2,325 | 3,0998 |
-7,5 | 2,4287 | 3,2380 |
-7 | 2,5366 | 3,3819 |
-6,5 | 2,6489 | 3,5316 |
-6 | 2,7657 | 3,6873 |
-5,5 | 2,8872 | 3,8492 |
-5 | 3,0134 | 4,0176 |
-4,5 | 3,1448 | 4,1927 |
-4 | 3,2813 | 4,3747 |
-3,5 | 3,4232 | 4,5639 |
-3 | 3,5707 | 4,7606 |
-2,5 | 3,724 | 4,9649 |
-2 | 3,8832 | 5,1772 |
-1,5 | 4,0486 | 5,3977 |
-1 | 4,2204 | 5,6267 |
-0,5 | 4,3987 | 5,8645 |
0 | 4,5840 | 6,1115 |
0,01 | 4,58780 | 6,11657 |
1 | 4,9286 | 6,5709 |
2 | 5,2954 | 7,0599 |
3 | 5,6861 | 7,5808 |
4 | 6,1021 | 8,1355 |
5 | 6,5449 | 8,7258 |
6 | 7,0158 | 9,3536 |
7 | 7,5164 | 10,021 |
8 | 8,0482 | 10,730 |
9 | 8,6130 | 11,483 |
10 | 9,2123 | 12,282 |
11 | 9,8483 | 13,130 |
12 | 10,522 | 14,028 |
13 | 11,237 | 14,981 |
14 | 11,993 | 15,990 |
15 | 12,795 | 17,058 |
16 | 13,642 | 18,188 |
17 | 14,539 | 19,384 |
18 | 15,487 | 20,647 |
19 | 16,489 | 21,983 |
20 | 17,546 | 23,393 |
21 | 18,663 | 24,882 |
22 | 19,841 | 26,453 |
23 | 21,085 | 28,111 |
24 | 22,395 | 29,858 |
25 | 23,776 | 31,699 |
26 | 25,231 | 33,639 |
27 | 26,763 | 35,681 |
28 | 28,376 | 37,831 |
29 | 30,071 | 40,092 |
30 | 31,855 | 42,470 |
31 | 33,730 | 44,969 |
32 | 35,700 | 47,596 |
33 | 37,769 | 50,354 |
34 | 39,942 | 53,251 |
35 | 42,221 | 56,290 |
36 | 44,613 | 59,479 |
37 | 47,121 | 62,823 |
38 | 49,750 | 66,328 |
39 | 52,506 | 70,002 |
40 | 55,391 | 73,849 |
41 | 58,413 | 77,878 |
42 | 61,577 | 82,096 |
43 | 64,886 | 86,508 |
44 | 68,349 | 91,124 |
45 | 71,968 | 95,950 |
46 | 75,749 | 100,99 |
47 | 79,709 | 106,27 |
48 | 83,834 | 111,77 |
49 | 88,147 | 117,52 |
50 | 92,648 | 123,52 |
51 | 97,343 | 129,78 |
52 | 102,24 | 136,31 |
53 | 107,35 | 143,12 |
54 | 112,67 | 150,22 |
55 | 118,23 | 157,62 |
56 | 124,01 | 165,33 |
57 | 130,03 | 173,36 |
58 | 136,29 | 181,71 |
59 | 142,82 | 190,41 |
60 | 149,61 | 199,46 |
61 | 156,67 | 208,88 |
62 | 164,02 | 218,67 |
63 | 171,65 | 228,85 |
64 | 179,59 | 239,43 |
65 | 187,83 | 250,42 |
66 | 196,39 | 261,83 |
67 | 205,28 | 273,68 |
68 | 214,51 | 285,99 |
69 | 224,09 | 298,76 |
70 | 234,03 | 312,01 |
71 | 244,33 | 325,75 |
72 | 255,02 | 340,00 |
73 | 266,11 | 354,78 |
74 | 277,59 | 370,09 |
75 | 289,49 | 385,95 |
76 | 301,82 | 402,39 |
77 | 314,58 | 419,41 |
78 | 327,80 | 437,03 |
79 | 341,48 | 455,27 |
80 | 355,63 | 474,14 |
81 | 370,28 | 493,67 |
82 | 385,43 | 513,87 |
83 | 401,10 | 534,76 |
84 | 417,30 | 556,35 |
85 | 434,04 | 578,67 |
86 | 451,33 | 601,73 |
87 | 469,21 | 625,56 |
88 | 487,67 | 650,17 |
89 | 506,73 | 675,58 |
90 | 526,41 | 701,82 |
91 | 546,72 | 728,90 |
92 | 567,68 | 756,84 |
93 | 589,31 | 785,68 |
94 | 611,61 | 815,41 |
95 | 634,61 | 846,08 |
96 | 658,34 | 877,71 |
97 | 682,78 | 910,30 |
98 | 707,98 | 943,90 |
99 | 733,95 | 978,52 |
100 | 760,00 | 1013,3 |
101 | 787,57 | 1050,0 |
102 | 815,86 | 1087,7 |
103 | 845,12 | 1126,7 |
104 | 875,06 | 1166,7 |
105 | 906,07 | 1208,0 |
106 | 937,92 | 1250,5 |
107 | 970,60 | 1294,0 |
108 | 1004,42 | 1339,12 |
109 | 1038,92 | 1385,11 |
110 | 1074,56 | 1432,63 |
111 | 1111,20 | 1481,48 |
112 | 1148,74 | 1531,53 |
113 | 1187,42 | 1583,10 |
114 | 1227,25 | 1636,20 |
115 | 1267,98 | 1690,50 |
120 | 1489,14 | 1985,36 |
125 | 1740,93 | 2321,05 |
130 | 2026,10 | 2701,24 |
135 | 2347,26 | 3129,42 |
140 | 2710,92 | 3614,26 |
145 | 3116,76 | 4155,34 |
150 | 3570,48 | 4760,25 |
175 | 6694,08 | 8924,71 |
200 | 11659,16 | 15544,27 |
225 | 19123,12 | 25495,40 |
250 | 29817,84 | 39753,85 |
275 | 44580,84 | 59436,23 |
300 | 64432,8 | 85903,3 |
325 | 90447,6 | 120587 |
350 | 124001,6 | 165321,9 |
360 | 139893,2 | 186508,9 |
365 | 148519,2 | 198009,3 |
366 | 150320,4 | 200410,7 |
367 | 152129,2 | 202822,3 |
368 | 153960,8 | 205264,2 |
369 | 155815,2 | 207736,5 |
370 | 157692,4 | 210239,2 |
371 | 159584,8 | 212762,2 |
372 | 161507,6 | 215325,8 |
373 | 163468,4 | 217939,9 |
373,946 | 165452,0 | 220584,5 |